A difficult week on and off the field for Arsène Wenger ended with some grudging cold comfort as Arsenal left it late to score a scrappy winner against a well-drilled and energetic Queen Park Rangers, Mikel Arteta prodding home from what looked, with the benefit of a replay, an offside position. In the process Wenger's team avoided a third scoring blank of the week, but still delivered a performance of notable entropy until a surge in the last 10m minutes, sparked by the sending off of Stéphane Mbia.

The encouraging midfield rhythms of early-season were almost entirely absent here. By the end Arsenal were even hanging on a little, Vito Mannone forced to save with his legs as Jamie Mackie beat three defenders and shot straight at the keeper.

"I'm very happy with the result," Wenger said. "We lost two big games and we were a bit jaded but we were serious and we moved the ball quite well. We needed to be patient against a QPR team that have quality, even though they are at the bottom. We were a bit lucky that they lost one player, it made it easier for us in the last 10 minutes."

The result leaves Rangers still clamped expensively to the bottom of the table and without a win. Mark Hughes may not, as the Arsenal support repeatedly insisted, find himself sacked in the morning, but he is a manager under gathering pressure, and here infuriated by a winning goal that left his team with nothing to show for a resilient performance.

"Arteta was offside twice," Hughes said. "He's offside on the initial header and then in the melee it comes back to him in an offside position and he scores. We've gone in and asked for an explanation and [referee Anthony Taylor] came up with some story about Ryan Nelsen playing everybody onside. I have no idea what he's going on about, but that's what you're up against. We've matched what they produced and prior to the sending off we looked most likely to win."

For Arsenal, fourth in the table now, there was also the encouragement of Jack Wilshere's return: a player charged with being, not just the future, but also the present in a midfield that has missed his snap and drive in recent weeks. Running out with a freshly clippered suede-head hairstyle on the day London's weather turned bitterly cold for the first time this season Wilshere's appearance was greeted with a genuinely affectionate cheer around a stadium that has of late been a place of fretful reflection. As Arsenal kicked off Wilshere's first touch – a familiar lithe, rolling, pigeon-toed pass out towards Lukas Podolski – was cause for the game's first concerted cheer. They started promisingly too, Olivier Giroud drawing a low save from Júlio César. Moments later Aaron Ramsey flicked a header on to the top of the bar.

Rangers were far from passive visitors as Hughes sent out a team of some attacking intent, with Shaun Wright-Phillips on the right of midfield and Junior Hoilett playing closest to Bobby Zamora in a 4-4‑1-1 formation.

Absorbing Arsenal's early thrusts, by midway through the first half the midfield pair of Esteban Granero and Samba Diakité were more than holding their own. As he had been against Norwich, Santi Cazorla was again surrounded here, the hulking Diakité shadowing him constantly in the first half. Giroud, linking with Podolski, produced a powerful skimming shot that César palmed away on 30 minutes, but by that stage it was the away fans producing a series of olés as Hoilett, Adel Taarabt and Granero took the chance to show that they, too, can keep the ball in tight areas.

Arsenal emerged with greater energy after the break and finally managed to disconcert César as Arteta's whipped free kick skimmed off the heads of Per Mertesacker and Zamora, drawing a clawing save from the Brazilian. With Rangers beginning to tire Theo Walcott and Gervinho – before he departed with an ankle injury – finally brought some drive to the flanks and Arsenal created the game's first clear-cut chance after 78 minutes. Walcott's cross struck Mbia on the back and fell to Cazorla unmarked and in space 10 yards out. He thrashed the bouncing ball horribly over the bar.

Then the match turned decisively Arsenal's way as Mbia was sent off, receiving a red card for a petulant kick at Thomas Vermaelen by the corner flag ("He deserved it," was Wenger's verdict). With Rangers now defending a very deep line Arsenal began to lay siege and the goal duly arrived on 83 minutes, Arteta poking home from a yard out after heading against the bar and then having the ball returned to him by Giroud. The scramble had been sparked by a fine cross from the right by Andrey Arshavin, another substitute. There were scenes not so much of jubilation as relief around the ground, repeated again as the referee blew full time on what has been a fraught week, albeit one spotted at the last with cautious note of hope.