"When you look at the game today, twice we had situations - once when 1-0 down and then when they came back to 2-2 - where we had to find the resources to win the game".
A Cedric cross from the right did not look particularly unsafe, but goalkeeper Petr Cech and defender Shkodran Mustafi left it to each other and Long nipped in to poke home.
For Southampton (18th place, 28 points), they are in the drop zone and three points from safety. Arsenal will rotate a few players to keep everyone fresh and healthy for the Europa League-or they should, at least-but today's match is still a very good opportunity to collect some points.
A goal line clearance came early, with James Ward-Prowse taking a feed from Shane Long and beating Petr Cech but not Calum Chambers.
There were two late red cards for Jack Stephens and Mohamed Elneny for pushing but Arsenal held on to secure a win that sees us close the gap on Chelsea to just two points.
Welbeck missed a great chance to put Arsenal back ahead when he fired over from three yards out after Wilshere had hooked the ball across goal.
There were chances at either end before Welbeck grabbed his first goal minutes before the break, only for Charlie Austin to rekindle the visitors' hopes after some brilliant work from Cedric.
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The home side soon found themselves in front as Welbeck scored his first league goal since September.
"We're disappointed we didn't get something out of the game but for me in terms of the performance I'm more than happy with that".
"We knew it was going to be a competitive game, Southampton are in a hard position", said Welbeck.
It took the Hammers only 17 minutes to take a 2 goal lead, and a third was deservedly added before the teams made their way back to the dressing room for half-time.