The pressure on the long-serving French boss intensified after Wednesday's 5-1 thrashing at the hands of Bayern Munich in the Champions League and anything but a convincing win over non-league opponents was unlikely to aid his cause.
In the end a goal in each half proved sufficient to keep alive hopes of a third FA Cup crown in four years, with Lucas Perez's fortuitous effort and Theo Walcott's 100th goal for the Gunners getting the job done.
Gander Green Land had been the scene of Sutton's fourth-round triumph over Championship high-flyers Leeds United and the National League strugglers – who have not won since defeating Garry Monk's side – performed admirably against top-flight opponents on Monday.
However, a major shock was never really on the cards as Arsenal's quality ultimately told, even if it was not the dominant display Wenger will have hoped for after their Allianz Arena debacle.
Roarie Deacon came closest to netting a dream goal for Paul Doswell's men, striking the crossbar just after Walcott's landmark goal.
Arsenal will now face Sutton's fellow National League side Lincoln City in the quarter-finals, while Doswell's charges return to the reality of a relegation battle with Saturday's trip to Torquay United.
Wenger's men struggled to create any chances of note early on, but their first attempt on target in the 27th minute saw them break the deadlock.
Perez cut inside from the right after a pass from Granit Xhaka, before sending in a low cross-cum-shot toward the far post that eluded the Sutton goalkeeper, with Walcott’s step-over seemingly putting off Worner.
9 - Lucas Perez has been directly involved in 9 goals in his last 8 starts for Arsenal in all comps (6 goals, 3 assists). Option.— OptaJoe (@OptaJoe) February 20, 2017
The away side unsurprisingly dominated possession as they went in search of a second goal against dogged opposition and Alex Iwobi should perhaps have made it two when presented with a gilt-edged chance from 10 yards out, only to see his placed shot deflected out for a corner.
Some poor play from David Ospina allowed Adam May a huge chance to draw things level in the dying minutes of the first half, but the Portsmouth loanee failed to get his shot on target as Arsenal escaped.
The visitors continued enjoy long spells of possession after the break and it was Walcott who doubled their lead in the 55th minute. Nacho Monreal sent in a fine low cross from the left and the England international coolly slotted home from close range after Iwobi failed to connect with it.
Sutton refused to throw in the towel, though, and Maxime Biamou and Jamie Collins were unfortunate not to pull one back, the former aiming straight at Ospina, while the latter saw his header go just over the crossbar.
Deacon was next to threaten for the minnows when he tried his luck from 25 yards out, only to see his stunning attempt come back off the bar before the ball was cleared into safety.
Arsenal even introduced Alexis Sanchez and Alex Oxlade-Chamberlain to further highlight the huge gulf in available resources between the two clubs and it is they who moved a step closer to Wembley, ending a historic run for Sutton, who certainly did not disgrace themselves on the big stage.