Both goals were of the kind in which the 34-year-old specialises, punched home from close range after others had done the spadework. They brought back distant memories for Egil Olsen, the Wimbledon manager. "I remember taking Norway's Under-21s to play England at Southampton many years ago and Cottee scored three times against us," he said.
It is mildly astonishing that Leicester remain a credible Premiership force given the feud that continues to rage behind the scenes. The break in fixtures did nothing to advance the cause of resolution, which neither side in a bitter boardroom dispute seems keen to embrace.
More shots were fired, from both directions, even as the manager, Martin O'Neill, prepared for this match. First, John Elsom, the incumbent club chairman, revealed the make-up of the board of directors he hopes to see in place after an Extraordinary General Meeting planned for next month.
Then it was announced that Elsom's ally, Sir Rodney Walker, chairman of Leicester City plc, had received notice from the plc chief executive, Barrie Pierpoint, the central figure in the opposite camp, that he had been declared persona non grata.
The letter from Pierpoint, a member of the so-called "gang of four" who hold sway in the boardroom, was unequivocally worded. "You would not be welcome on this occasion or on any other occasion in the future," Sir Rodney was told. He stayed away to avoid any "unsavoury incident" but Elsom immediately disassociated himself from the letter, which he described as "outrageous and petty".
Pierpoint has been trying to seize power for many months but matters came to a head at a stormy plc board meeting on 10 September at which Pierpoint and his allies say Elsom and Sir Rodney verbally resigned, a claim they fiercely deny.
The battle will be won or lost at the EGM but it is unlikely to take place before 20 December. Pierpoint, in any event, seems to face a near impossible task if he is to gain the support needed to oust Elsom, since the hugely popular O'Neill has placed himself in the Elsom-Walker camp.
O'Neill made no comment yesterday. Remarkably, he keeps the minds of his players on football, as they demonstrated again yesterday when they responded to Wimbledon taking the lead by equalising within seconds.
In an appropriately low-key contest, the London side went ahead when an aimless-looking ball from Jason Euell dropped nicely for Marcus Gayle to volley home his fourth goal of the season. But, almost from the restart, O'Neill's team drew level, Robbie Savage stretching himself to keep Emile Heskey's deep cross in play and in doing so setting up the ever-alert Cottee to squeeze his seventh of the campaign past Neil Sullivan.
A mistake by Dean Blackwell on the left, failing to cut out Steve Guppy's pass in a swirling wind, allowed Heskey to create a second goal 13 minutes into the second half, the England forward flicking the ball across goal before Sullivan reached it. Again Cottee was in the right place.
After Gerry Taggart's interception of Carl Cort's cross preserved the advantage, Heskey came within a bootlace length of adding a third when he attempted to deflect Guppy's low cross. Cottee, unusually shooting from distance, missed his hat-trick by a coat of paint.