Paul Pogba may have been making his second debut for the club, this time as the world's most expensive footballer, but it was Ibrahimovic who stole the limelight as he made it three Premier League goals in two games for United.
The Swede opened the scoring after 36 minutes, and added a second after the break from the penalty spot to secure a second straight win for Jose Mourinho's side, who were already top of the table heading into the match.
For Southampton, who had won their last two trips to United 1-0, it was a disappointing evening that saw new boss Claude Puel left with just a point after two games.
There was plenty of excitement around Old Trafford as Pogba was named in the starting line-up by Mourinho, but his first touch of the ball looked a far cry from one belonging to the world's most expensive player.
Less than a minute after kick-off, the Frenchman completely miscontrolled a simple pass into feet which allowed Southampton to launch a counter-attack. Luckily for him, the Saints failed to capitalise.
Pogba quickly caught up with the pace of the game, though, and forced a decent stop from Fraser Forster after 13 minutes, picking up the ball in the Southampton area before seeing his curling effort kept out by the goalkeeper.
Southampton were more than happy to allow United possession as they threatened on the counter-attack, with Nathan Redmond looking particularly lively in the early stages, but they lacked a cutting edge and never truly threatened David de Gea's goal.
Manchester United then switched up the gears as the half carried on, and the first incisive moment brought the first goal of the season at Old Trafford.
Wayne Rooney, given far too much space on the right, looked up before whipping an absolute pearler of a cross into the path of Ibrahimovic at the far post, who rose highest above Jose Fonte to power his header past Forster.
Manchester United have never lost a Premier League game at Old Trafford when leading at half-time, and Southampton's chances of ending that run became even more unlikely seven minutes after the break.
Jordy Clasie, on for the injured Oriol Romeu in the first half, daftly brought down Luke Shaw in the penalty area, and Ibrahimovic stepped up to slot the ball into the bottom corner.
The rest of the match was largely a formality for United, but Pogba missed a glorious chance after 64 minutes to open his account and completely kill the game as a contest.
The Frenchman beat his marker in the air to get on the end of Juan Mata's corner, but he could only head the ball over when he should at least have hit the target.
Pogba then had another chance late on as United countered in stoppage time, but he could only fire wide from Henrikh Mkhitaryan's pass after being teed up on the edge of the area.
