Hull won for only the second time in the Championship this season as they beat Luton 3-0.
A quiet opening 20 minutes saw precious few chances at either end, Harry Cornick's effort deflected behind for the hosts and then Hull's Tom Eaves unable to divert a loose ball into the net from close range.
Town's Andrew Shinnie wasted his side's best chance, slamming well over the bar from just outside the box after being teed up by Cornick's cut back.
In the second period, former Liverpool youngster Stewart rifled over from 20 yards for the visitors.
From his next attempt on 63 minutes, he was to break the deadlock, as Grosicki escaped on the left.
The goal certainly buoyed City, and Grosicki's snapshot from 20 yards was inches wide, while the previously-quiet Jarrod Bowen then curled over the top.
Hull should have sealed the win with five minutes left, Bowen putting Grosicki in the clear, but from eight yards out and with just Sluga to beat, he rolled wide of the target.
Luton then almost made then pay instantly as Shinnie swung over a free-kick and Potts glanced his header off target.
With three minutes to go, Hull made sure of the points when his time Grosicki did have his radar switched on, cutting in from the left and then beating Sluga at his near post.
It went from bad to worst for the hosts in the final minute, as they conceded a goal of pure comedy late on, Bowen racing away once more to have just Sluga in his sights.
The keeper did well to save, but then when trying to gather the loose ball, saw Potts decide clear the ball against him and it spun backwards and in, though Stewart did try and claim it on the line.