Far from discouraging Gianluca Vialli, who was sent off in the same game, Sutton's abrasive attitude and reaction to his roughing up endeared him to the Chelsea manager. Enough for him to bring the deceptively slight, 6ft 3in striker south from relegated Blackburn for a club record pounds 10m, not merely for his goals but his "mental toughness".
"When you play you have to be committed, and being big, even if you're having a stinker, you can always put yourself about," Sutton recalled with a rueful smile when we met at his west London hotel, home for him and his wife Samantha and three young sons until their new pounds 1m Hertfordshire home is vacated.
Dennis Wise was no stranger to him, either, and Sutton soon felt the humorous edge of his tongue in training when the ambassador of the British quarter at Stamford Bridge jested to universal laughter after an abberation by the newcomer: "I hope Ken Bates kept your receipt!" He added: "When we played against Dennis we all used to dislike him. He was one of those horrible, niggly players. I'm sure a lot of players round the country would agree. But off the field he's really a very nice guy."
So, too, the remainder of Chelsea's multi-culture club, where Sutton has already discovered an esprit de corps in pre-season training. "It is strange being with so many foreigners," he said, "but team spirit is good and the first thing I picked up on is that all the players do get on well." But, like mock exams before the real thing, it is this weekend's kick-off against Sunderland when the real trial of his, and Chelsea's, resolve will begin. Ten million takes a lot of justifying in itself, not to mention joining a team with serious championship pretensions. Many pundits are convinced it is already Chelsea's by decree, with the extra impetus provided by Sutton and the Frenchman Didier Deschamps.
Even in such inflationary times, such a bounty on the head could be the the ruination of some. Yet Sutton had precisely the same expectations made of him in the summer of 1994 when Kenny Dalglish enticed the then 21-year-old from Norwich for pounds 5m and, in doing so, created the celebrated SAS partnership with Alan Shearer, scorers jointly of 49 championship goals. "It is a big fee," he agreed. "But I don't look at it as such a problem as I did five years ago when I really did feel the pressure. I took a hell of a lot of flak at first at Blackburn. It helped me that we did win the title that same year."
Sutton added: "It was nice to prove people wrong, the ones that wrote me off when I played my first couple of friendlies and were saying `How much?' and rub their faces in it. It's different this time. Now I look at things much more positively, and I'm much more relaxed. The money side is irrelevant. You can only go out and play the best you can. Goals have never been the be-all and end-all for me because I've always been a target-man kind of player, but if I get 20 goals I'll be happy. If you're fazed by the fee, the chances are you'll go under.
"Coming here I've moved to a club with great, established players, who've won World Cups, European Cups, players with wonderful technique who've won everything there is to win, and I'm certain it will bring my game on. I can look at Gianfranco Zola and I can learn things from him. The same with Tore Andre Flo, who has tremendously quick feet for a big man."
Sutton, a family man who relaxes by walking his four dogs, is also very much his own man. He would not be averse to moving abroad at some stage. "It's good to broaden your horizons, but I don't really need to at Chelsea, do I?" he responded with a rare crease of his features.
Some interviewers have found him prickly, a perception exaggerated by his tendency to frown before answering. The reason is an inclination to engage brain before activating vocal cords and a refusal to be enveigled down potentially hazardous discussion paths. Yet, he can also be surprisingly forthright, even on the one subject he would rather not be reminded about.
One day maybe Sutton will actually be remembered for the goals he scored for his country rather than as the man who, to some minds, should be standing at traitors' gate, having refused to play for England. Terry Venables was just one who questioned his decision back in the winter of 1997, claiming: "It raises doubts about desire, motivation and ambition. To me it defies understanding." Maybe this season, if his international career takes the upturn he believes it will, such doubts will be erased for ever.
Frankly, one England cap is pitiful reward for a man of his talents and experience. "One cap," he repeated sardonically. "Yes, 10 minutes against Cameroon. Can't remember much. I think I got about two touches. It was nice, but I'd have liked a lot more."
Was that not, you suggest, the result of his own obduracy and arrogance when he spurned the opportunity of an England B team shirt, having just made his first-team debut? "That's just the way I saw it at the time," he explained. "I am fairly instinctive, though not to the detriment of doing real harm to myself. I just felt that I was worthy of a place on the basis that I'd been in the previous squad and I'd done well.
"Then players had seemed to get ahead of me and I'd been relegated. I spoke to Glenn Hoddle and I didn't get a great deal of positive feedback. I'm patriotic and it's a great honour to play for England. But there are times when you have to stand up for yourself and do what you think is right.
"In many ways I do regret making that decision because of what happened afterwards. I'm not sure if I would make the decision again now. You can't say unless it happens. Maybe I would have had a few more caps if I'd gone and played in that game."
This year's England recall by Kevin Keegan came as a surprise. "The brightest spot that I had last season which otherwise was a nightmare." But, now, having become part of a splendid Chelsea lineage of forwards, which traces back to Roy Bentley, through Bobby Tambling, Peter Osgood, Kerry Dixon, Vialli and Zola, his claim to an England berth will be irrepressible, assuming he secures a regular club place.
There are 10 million reasons why he should, but Sutton is making no assumptions. "Not with two well-established internationals like Zola and Tore Andre Flo, or Mikael Forssell, who is an unbelievable talent for someone only 18," he said. "I've come here for the competition, as well. It's good for my career to be fighting for a place. It never gets to me if I don't score. There's always another chance around the corner. I look at someone like Alan Shearer who's got tremendous toughness. They've knocked him over the years but he's always bounced back. People are trying to shoot him down now, but he has real resilience."
Vialli is another source of inspiration. It was the lure of the Latin's reputation which convinced Sutton that his future lay in west London. "It's similar signing for him as signing for Kenny Dalglish," he enthused. "It's always good for a striker to join a club whose manager has played in the same position.
"I was sad to leave Blackburn, and I enjoyed playing under Roy Hodgson. I fancy them strongly to come back next year. At my age, if you do need that push to play international football, you have to play in the Premiership. It was very difficult for Brian Kidd to take over at the stage he did, with a depleted team. He turned it round for a time, but that was more due to grit than playing well."
When it came to a choice of clubs, Sutton was all too aware of the championship promise Vialli's team had exhibited last season. "I thought they were unlucky not to go the whole way. This season, it will still be hard to knock Manchester United and Arsenal off their pedestals, but the championship could be really competitive. Tottenham look a strong unit this year, Leeds did well and Liverpool have bought lot of players. It won't be a great surprise if any of those did well.
"There are a lot of downs in football, but when things go well there's no better feeling. It was nice to win the title with Blackburn so quickly. Hopefully, I can do same at Chelsea."