The Hatters moved back into the top half of the table, and above their hosts, with a perfect away performance as Cornick netted in both halves to give Nathan Jones' side a cushion that goalkeeper Sluga preserved with a save from Jed Wallace's penalty in the closing stages.
Manager Nathan Jones made one change from the team that drew with Huddersfield in the final game before the international break, with Pelly-Ruddock Mpanzu coming back from injury in place of Luke Berry.
Fred Onyedinma was making his return to the matchday squad against his former side, and there was also a spot amongst the substitutes for Admiral Muskwe after he played an hour for the Development side earlier this week.
Millwall had the game's first attempt on goal with nine miunutes on the clock, Jed Wallace evading the Town back four's call for offside, but shooting straight at Simon Sluga.
Within two minutes, the Hatters were in front. Tom Lockyer clipped a long ball up the right, where Elijah Adebayo challenged Jake Cooper, whose header fell into James Bree's path.
The former Aston Villa man drove forward towards the Millwall bos, assisted by Jordan Clark, who rode Lions skipper Shaun Hutchinson's tackle and slipped the ball to his left, where Cornick bent a glorious shot first time into the top corner.
A superb passage of play almost brought a second on 20 minutes, when a 12-pass move ended with Adebayo playing Bree into the right side of the box, but the wing-back's low cross was just too far ahead of Cornick coming in at the far post.
Clark then volleyed over the bar, before Millwall rallied, a low cross from the right falling to Benik Afobe, who was denied by a perfectly timed block from Lockyer as the Town defenders put their bodies on the line for the cause, captain Sonny Bradley rising highest to head the resulting corner clear.
Lockyer was soon in the wars, producing two more blocks in quick succession to deny Sheyi Ojo inside the six-yard box with the half-hour mark approaching, and that resolute defending continued until the end of a positive first half for the Hatters.
Within eight minutes of the restart the afternoon became even more positive, and once again it was Cornick who delivered. Mpanzu smuggled the ball out of the pack on the left, nutmegging George Saville to release Clark, who once again provided the inch-perfect assist for Cornick.
The forward let the ball run in front of him then, from just inside the area, produced a pinpoint first-time finish across Bartosz Bialkowski into the bottom corner for his sixth goal of the season.
It was almost three in the 58th minute when Naismith won the ball off Afobe midway inside the Millwall half and shifted it sideways to Mpanzu, who unleashed a venomous shot that beat Bialkowski all ends up, only to rebound back off the crossbar.
Cornick went off to a standing ovation from the travelling fans midway through the half, replaced by Cameron Jerome, and it was Millwall - having introduced towering striker Matt Smith - who had the next attempt on goal, although Cooper's tame 73rd minute header was easy for Sluga to deal with.
Clark went into referee Chris Kavanagh's book for a foul on Ojo, and Wallace managed to get his 30-yard free-kick over the wall and on target, but the Croatian keeper dived full length to his left to push it around the post.
Clark was taken off with just under quarter-of-an-hour to go, with Henri Lansbury on in his place, then Muskwe was introduced for Adebayo moments later.
Millwall thought they'd been handed a lifeline eight minutes from time when Naismith was penalised for handball in the box, when it looked like he'd been pushed by Smith. Sluga produced another brilliant save, diving to his right, to push Wallace's kick away.
The win makes it three unbeaten, and one defeat in eight matches for the Town, who head to Derby on Tuesday night in 10th place.
Goals:
Town: Cornick 11, 53
Att:
14,227 (1,631 Hatters)
