The 31-year-old leader of Joe Kinnear's pack was once again at his combative best as the Dons moved up to second place in the Premiership with a win that took their remarkable unbeaten run to 18 matches.
And while Jones laughed off suggestions that Wimbledon can upset the title odds by wrestling the Premiership crown away from the likes of Manchester United, Newcastle, Liverpool and Arsenal, he saw no reason why they should be daunted by the challenge of Europe.
"We would be crazy to think about winning the Premiership, though, and to be fair we're not the sort of lads who would do," Jones said after two goals by Efan Ekoku - their new leading goalscorer - and another by Dean Holdsworth had sentenced the Roker men to only their second home defeat of the season.
"Europe does appeal to us, but even that's a long way off. But it wouldn't be such a big thing to our players anyway because most of our lads have played for their countries at full, B or Under-21 level and even the Premier League has a European feel about it now."
Joe Kinnear dismissed reports that he has been targeted by both Blackburn and Manchester City and indicated that he would not quit his London roots anyway. "I've not had any contact with either Blackburn or City and I'm proud of the fact that I am the second-longest serving manager in the Premier League behind Alex Ferguson," he said.
"I've been here seven years and it's taken me a long time to put this team together. It has seven homegrown players in it, it's the strongest squad I've ever had and it shows you what can be achieved with hard work."
Goals: Ekoku (8) 0-1; Ekoku (29) 0-2; Melville (83) 1-2; Holdsworth (89) 1-3.
Sunderland (4-4-2): Perez; Kubicki, Melville, Ord, Scott; Rae (Gray, 81), Bracewell, Ball, Kelly (Bridges, 52); Smith, Russell. Substitutes not used: Agnew, Hall, Preece (gk).
Wimbledon (4-4-2): Sullivan; Cunningham, Perry, Blackwell, Kimble; Ardley, Jones, Earle (Harford, 77), Leonhardsen; Ekoku, Gayle (Holdsworth, 74). Substitutes not used: Clarke, Fear, Murphy (gk).
Referee: K W Burge (Tonypandy).
Bookings: Sunderland: Rae. Wimbledon: Earle, Jones.
Man of the match: Ekoku.
Attendance: 19,672.Reuse content