It may be assumed that no one craves a trophy more this season than Alan Shearer in his valedictory campaign, and it was the Magpies' modern talisman who struck the decisive blow, moving a step closer to Jackie Milburn's club record of 200 goals with his fourth of the season - 196th all told - some 10 minutes from time.
However, it was a moment soured by bad feeling. Shearer's anger at a first-half challenge by the Grimsby captain, Justin Whittle, spilled out even after the final whistle, when the furious Newcastle captain eschewed any pretence at diplomacy in condemning an elbow-led assault by the home player, which left him needing three stitches in a cut lip at half-time.
"It was blatant yet the referee, who was five yards away, did nothing," Shearer said. "It would have been easy for me to stick one on him because that is what I wanted to do but the better away to answer it was to come away with a goal and a victory."
Whittle had been on the receiving end of an earlier challenge from Shearer but the apology offered by Shearer appeared to count for nothing. His anger was shared by Souness, who spoke to the referee, Mark Halsey, about the incident at half-time.
"I've rarely seen Alan so angry," Souness said. "It was a very dangerous challenge and it was fitting he should have the last word by scoring the winning goal."
The Grimsby manager, Russell Slade, insisted that if Whittle's conduct had been outside the spirit of the game it was out of character. "I did not see the incident but Justin has an exemplary record in disciplinary matters," he said.
"All I can say, without having seen the television replay, is that both he and Alan Shearer are competitive individuals and that sometimes in a cup tie you can get a very bruising encounter. I hope [the incident] does not overshadow the game because I was very proud of the way my team performed."
None the less, the second-round conquerors of Tottenham could not quite raise their game enough in front of a raucous full house at Blundell Park, a ground with happy memories for Newcastle, who clinched promotion to the Premier League on their last visit, in 1993. The striker Gary Jones momentarily had the crowd on their feet when he headed a first-half free-kick wide, but Newcastle generally had their measure.
Shearer's decisive strike came when he took advantage of a slip by Paul Bolland after Michael Chopra had made a incisive run along the right to score with a powerful strike.
Grimsby Town (4-4-2): Mildenhall; McDermott, Whittle, G Jones (Gritton, 71), Newey; Cohen, Kalala, Bolland, Andrew (Parkinson, 71); G Jones, Reddy. Substitutes not used: Ramsden, Barwick, Toner.
Newcastle United (4-4-2): Given; Ramage, Taylor, Bramble, Babayaro; Solano (Clarke, 72), Faye (Brittain, 72), Parker, N'Zogbia; Chopra, Shearer. Substitutes not used: Caig (gk), Elliott, Boumsong.
Referee: M Halsey (Lancashire).