The substitute, Olivier Giroud, completed the win with a sweet finish into the far corner and, suddenly, Wenger's claim that the top four looked "perfectly possible" gathered fresh momentum.
West Ham's loss to Arsenal is their fifth in a row in the league, which Slaven Bilic reiterates they must halt immediately.
It was Arsenal's first league win since February 11. "We wanted to do it before this game against Swansea". "We have been in this situation before, although probably not as bad".
"But the second half started like the first half finished, they were again too often, too soon there, and after the first goal it's hard to come back".
"I'm convinced the supervisor is going to have strategy in motion and who understands - we've done it in days gone by", said the 28-year old.
"There has been huge pressure on the players in recent weeks and I'm happy that they can come back and focus and enjoy their game".
Wenger's pre-match mood was not improved by injury robbing him of goalkeepers Petr Cech and David Ospina, which handed a rare Premier League start to Emiliano Martinez. "We are always praised maybe more than we deserve it when it goes well and punished more than we deserve it when it doesn't go well, but that's our world".
His confidence is based on the belief that Arsenal have been playing more freely over the past two matches.
Defeat to Arsenal on Wednesday night left the club within just five points of the relegation zone, making Saturday's clash with relegation rivals Swansea a vital three-point affair.
"We know deep down that we have to forget about that as quickly as we can and get a win on Saturday".
"They were thinking they were going to be in Europe so they brought in players that would supplement the squad who had played European football". We need one win and it will change everything for us.
"I will never stop believing in myself but to get, or to keep, other people believing, people who are not involved in training or the amount of work I do here, you have to deliver the results and now it is about time".
"They take risks, they stay up with a few players and every time you lose the ball or when they get the ball it's a problem for the defence with those really good players, great players, on such a big pitch".
6 arrested for terrorism in wake of St. Petersburg bombing
He has named Daesh as one of the reasons behind Russia's military campaign in Syria in support of Syrian President Bashar Assad. Earlier on Thursday, mourning continued in St Petersburg as the jittery city laid to rest the 14 people killed in the attack.
Cubs' Baez collides with Heyward year after Schwarber injury
This is a game I see Chicago bouncing back and running away with, so I'll take them on the run line to give my bet more value. Baez gave up a thumbs up and was able to walk off after the play, but the Cubs understandably removed him from the game.