There were only a few minimal chances in the opening 45 minutes, with opportunities for Paul Pogba and Shane Long before Ibrahimovic opened the scoring.
The Swede added a second just after the restart, that is when United stepped up their game, with good opportunities for Anthony Martial and Pogba, but Ibrahimovic's two goals proved to be enough on the night.
Return starting off slow
United fans lucky enough to be inside Old Trafford, and fans all over the world were hotly anticipating the second debut of world-record signing Pogba.
It was the Frenchman who in fact had United's first real opportunity of the game. He received the ball from Ibrahimovic and, despite the angle, had a crack at goal, and he managed to sting the palms of Fraser Forster.
Southampton were determined to ruin the night of celebrations at the Theatre of dreams, and came incredibly close to doing so. A free-kick came to the feet of Long, who did well to turn quickly, but his shot only found the side-netting - much to the disappointment of a small contingent of Saints fans who were celebrating.
Enjoying life in England
Many questioned if Ibrahimovic would be capable of performing at the same level that he has across his career.
But despite it been early days, he has made a great start, and continued that by opening the scoring in the 36th minute.
It was good play from United, with Antonio Valencia playing out to Wayne Rooney, the skipper produced a great cross to the far post, and the running Swede thumped a header into the bottom corner.
Going one better
Claude Puel's side offered very little in the attacking side of their play, but thought they had an equaliser just after the restart.
A cross into the area found the head of Dušan Tadić, who did well to turn in to home, but the flag was immediately up for offside.
United continued their dominance, with Martial testing Forster, but were handed the chance of a second when they were given a penalty.
Luke Shaw produced an excellent run into the area before been clipped by Jordy Clasie, which left Anthony Taylor with an easy decision.
Ibrahimovic stood over the spot-kick and made no mistake by smashing it into the bottom corner, for his fourth goal in three games.
Turning the screw
United were displaying some excellent attacking football, which had been somewhat missing since Sir Alex Ferguson's departure, and were proving a danger as they looked for their third goal.
Fans were hoping for a debut goal for Pogba to wrap a fantastic performance, and almost had it after the hour mark as he got his head to a corner, but the effort was over the crossbar.
United produced some scintillating counter-attacks in quick succession, but Saints stood firm. The first came from Martial, as he blazed into the area after Rooney's through ball, but Forster did well to save, and was there again to cut out Shaw's cut-back, but the night belonged to Ibrahimovic and United.