Arsene Wenger had made seven changes with Thursday's Moscow decider in mind and though the visitors were under pressure again early on, Tadic cynically clattering Reiss Nelson when the youngster dropped a shoulder, the game's first chance fell their way as Arsenal switched off.
The England worldwide had found the net in the first half too, his deflected drive making it 2-1 after Pierre-Emerick Aubameyang's poked finish had cancelled out Shane Long's early opener for the visitors.
Welbeck put the Gunners ahead ten minutes later, with a powerful shot from just outside the box that glanced off of Maya Yoshida and went looping over McCarthy.
Welbeck headed home the victor in the 81st minute to settle an eventful game at the Emirates, having previously made it 2-1 with a deflected shot in the first half.
Mohamed Elneny was also shown red before the end of the game, for a lighter push on Southampton fullback Cedric Soares.
But Welbeck had the last word - and neatly distilled his Arsenal career - by making amends for a missed open goal seconds earlier by nodding in Iwobi's floated cross to the back post.
Super Eagles forward, Alex Iwobi, was involved in two out of Arsenal's three goals that saw of Southampton in a Premier League encounter at the Emirates Stadium on Sunday.
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It is just one win in 19 league matches now and they have conceded six goals in two league games since Hughes replaced the sacked Mauricio Pellegrino in the middle of March.
In fact, only Wayne Rooney (seven) and Robin van Persie (six) have scored more Premier League goals against Petr Cech than Shane Long (five).
"I'm happy with the assist, glad to get the goals".
It took us some time to get to the pace of the game.
"The advice I'd give my youngster self is to always believe in what you're doing".
The game looked to be petering out before an on-field coming-together between Jack Wilshere and Jack Stephens led to the latter being sent off.