The futures of Ozil and Alexis Sanchez remain uncertain with the Arsenal duo entering the final 18 months of their current deals.
But both were central figures as Arsene Wenger's team secured the two-goal margin of victory that lifted them above Chelsea on goals scored.
Ozil's stunning second-half header, a goal that came about in controversial circumstances in the eyes of Stoke manager Mark Hughes, was the highlight of the win.
Arsenal had fallen behind to Charlie Adam's 23rd-minute penalty but levelled before half-time thanks to Theo Walcott's 10th goal of the season.
Ozil and Alex Iwobi struck after the break to shift the pressure onto Chelsea 24 hours before Antonio Conte's side host West Bromwich Albion.
Wenger had complained angrily about referee Lee Mason's decision to award a penalty after Stoke's Joe Allen was floored by a leading elbow from Granit Xhaka.
But it was Hughes' turn to complain when Ozil scored in space vacated by Stoke left-back Erik Pieters, who was out of position after receiving treatment at the other end of the pitch.
Arsenal had started the game positively, finding plenty of room down the right hand flank. But for the most part, Stoke managed to restrict the home side to the occasional half-chance before they took the lead through Adam's penalty.
Shortly before the Scotland international gave the visitors the lead, the midfielder had shown his quality with a lofted ball that allowed Marko Arnautovic to set up an opportunity that Allen sent wide.
And Adam showed impressive composure to send Cech the wrong way from the spot after Allen had been floored by Xhaka in a clumsy challenge between the pair.
Arsenal's problems increased when Shkodran Mustafi was forced off with what appeared to be a hamstring injury and the introduction of Hector Bellerin prompted a reshuffle of the home back-four.
But the substitute's most significant first half contribution came at the other end of the pitch when he produced the cross that led to Walcott's 42nd-minute equaliser.
Stoke had continued to appear vulnerable on their left hand side, with Allen providing only limited cover for Pieters.
The left-back was isolated once again when the ball was played out to Bellerin from a central position and the Spaniard drilled in a low cross that was turned home by Walcott at the near post.
The goal brought relief for Wenger and his players who had been growing increasingly frustrated in their efforts to cancel out the controversial opening goal.
But it was soon the visitors' turn to feel hard done to when they fell behind to Ozil's clever, looping header.
Moments before, Stoke had pressed forward with Pieters requiring treatment after clashing with Bellerin as he went for a far post header and the left-back had not recovered his ground when Alex Oxlade-Chamberlain picked out Ozil with a floated pass.
There was no doubting the quality of the Germany international's finish but the playmaker was helped by Pieters' absence.
While Stoke fumed, Arsenal continued to press with Xhaka and Oxlade-Chamberlain both testing Grant with long-range shots.
But Arsenal were unlikely to squander the lead and finally established the two-goal advantage they needed to go top when Iwobi picked up the loose ball after Sanchez had been fouled on the edge of the Stoke area.
The referee played the advantage, allowing the Arsenal youngster to wrap up the points with a right-foot finish.