Wenger made seven changes from the side that beat CSKA 4-1 in their quarter-final first leg on Thursday with securing a return to the Champions League by winning the Europa League now Arsenal's priority for the rest of the season.
The Gunners are now just three points behind their London rivals with six games left to play.
Sunday's triple means that Arsenal have hit three goals or more in five successive home games for the first time since 1958-59, nearly 60 years ago.
However it was Southampton that started brightly. After a scrappy start in rainy conditions, Southampton were the first to threaten - and only Hector Bellerin denied them the opening goal. The Irishman prodded home in front of a lacklustre home defence lacking leadership, anticipation, positioning and tactical coherence after a cross from the right by Cedric. "That shows when Danny is fit, and can play week in, week out, he comes back to his level".
Second half substitute Charlie Austin made an immediate impact as he came off the bench to draw Southampton level on 73 minutes but Welbeck nodded in the victor nine minutes from time. When Welbeck somehow contrived to scoop the ball over the bar from three yards soon after, Arsenal supporters must have feared their chance to win the game had gone.
"If they can show the kind of belief, and fight, in their remaining fixtures I think they might get out of trouble".
Welbeck's deflected shot then made it 2-1 to the host before half-time.
The defender's reaction - a blatant shove on Wilshere, who had performed the role of wind-up merchant to perfection - left referee Andre Marriner with no option but to send him off.
And as Marriner blew for the final whistle, yes it was an entertaining match, and yes it gained a result.
Throughout the ill-fated reign of Mauricio Pellegrino, many Southampton fans had been vocally in favour of their team using two forwards to solve their attacking problems.
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