Before the match, all the talk was about another one of Manchester United's high-profile signings. Paul Pogba made his second Manchester United debut, but it was Zlatan who stole the headlines.
It was a fairly even encounter on the whole, with Manchester United having the better of the early stages of the game without creating any clear-cut chances.
Pogba threatened to make it a dream debut on 13 minutes, but the Frenchman's deflected shot was comfortably saved by Fraser Forster.
Just before the half-hour mark, Southampton had their best chance of the half, but Shane Long fired his effort just wide.
Not long after Long's effort, Ibrahimovic had his first sight at goal. The Swede attempted an acrobatic overhead kick, but his effort floated wide.
However, the former PSG man did not have to wait long to get on the scoresheet. Just seven minutes later, Rooney crossed from the right and Ibrahimovic rose above the Southampton defence to fire a powerful header past Forster.
Less than five minutes after half-time and Southampton had the ball in the back of the net when Dusan Tadic headed past De Gea, but the winger's effort was ruled offside.
This seemed to be the point where things started top get worse for Southampton. Just one minute later and Clasie fouled Shaw in the area, and up stepped that man Ibrahimovic once again.
The striker powered his penalty home to Forster's right, with the former Celtic 'keeper diving the wrong way.
Just before the hour mark, Nathan Redmond had a chance for Southampton, but the former Norwich man hit his effort wide.
Pogba almost got on the scoresheet on 64 minutes, the Frenchman met Mata's corner, but headed over the bar.
Southampton did have a couple more chances. Shane Long headed just past the far post with 15 minutes to play, and Tadic had another chance with three minutes to go, but once again fired wide.
Overall, United won the game mainly due to their superior finishing. Ibrahimovic took his first goal brilliantly and made no mistake with the penalty. Southampton were by no means outplayed by United. The Saints had plenty of chances, but their failure to finish was their ultimate downfall.