Last year, under Dalglish, they reached the final and last night they moved to within two games of a return trip to Wembley when Louis Saha scored the only goal in this fifth-round replay. The reward is a home quarter-final against Everton.
The result extends a dismal record for Blackburn, who have gone out of the Cup by losing at home on the last six occasions, five of them after they had gained replays.
Stripped half bare by injury and ineligibility, Blackburn rarely threatened to knock Newcastle out of a stride personified most elegantly by the German midfielder Dietmar Hamann.
Indeed, Newcastle would have spared their blood pressure if they had taken their chances on the break towards the end. Fortunately for them the goal by Saha, a French striker on loan from Metz and playing only because Alan Shearer was injured, proved enough.
"It should have been more than 1-0," Gullit, the Newcastle manager, said. "Finished. The performance was right. We were in control which pleased me and you never had the feeling we were in trouble."
Rovers, dreadful against Sheffield Wednesday on Saturday, were an improvement but only really threatened at the extreme ends of the first half.
"We patched it up and that doesn't help," Brian Kidd, their manager, said. "We're continually making four or five changes and it's difficult to create a pattern. It's unfair on the players. It's makeshift."
Kevin Davies should have done better with a header from Nathan Blake's knock-down after three minutes. But, 11 minutes later, off balance and at an acute angle, he did well to frighten John Filan.
It had been a bright start for Rovers, but slowly Newcastle's passing game wrestled control from the more frantic Blackburn. After 15 minutes Filan reacted smartly to parry a 30-yard free-kick after the defensive wall had parted for Hamann, but if he showed sharpness then it was little compared with eight minutes later when he dived low to his left to turn to Temur Ketsbaia's shot round the post.
The impression was that Newcastle were gaining control and that was underlined after 39 minutes when the visitors took the lead. Again Hamann was to provide the pass, 40 yards from right to left into the gap behind Jeff Kenna. Saha surged into that hole, controlled with his chest and then half-volleyed sweetly into the far corner.
This instigated a response from Blackburn and the closest they came to an equaliser arrived a minute later. Kenna's pass was met on the charge by Jason Wilcox, whose touch would have crept in at the near post but for Shay Given's excellent save.
The second half was a tale of unconvincing Blackburn pressure and Newcastle breaks, some of which ought to have produced something more tangible. Never was this more so than in the 66th, when Garry Brady lashed a shot that was saved by Filan and sat up invitingly for Laurent Charvet, who struck the outside of the post. Just before then Blackburn had gambled by bringing on an extra striker, introducing Ashley Ward for Damien Duff.
The decision prompted boos from the home crowd, summing up a bad night for Rovers. Kidd's extended honeymoon could be coming to an end.
Blackburn Rovers (4-4-2): Filan; Kenna (Croft, 56), Peacock, Broomes, Davidson; Gillespie, Marcolin, Wilcox, Duff (Ward, 58); Davies, Blake. Substitutes not used: Johnson, Dunn, Flowers (gk).
Newcastle United (4-4-2): Given; Charvet, Dabizas, Howey, Barton; Solano, Hamann, Speed, Brady; Saha, Ketsbaia. Substitutes not used: Lee, Dalglish, Hughes, Griffin, Harper (gk).
Referee: D Gallagher (Banbury).