The Swedish striker headed home from Wayne Rooney’s cross from the right.
He scored a fourth goal in three matches from the penalty spot after Jordy Clasie tripped Luke Shaw.
Paul Pogba, United’s £89m world-record signing from Juventus, made an energetic full league debut.
Ibrahimovic’s force of personality could be every bit as much of an asset as his ability to United this season.
The 34-year-old, signed on a free transfer after leaving Paris St-Germain at the end of last season, marked his home debut with a confident display that brought warm appreciation from the home supporters.
Having scored in the Community Shield win over Leicester City and United’s Premier League weekend victory at Bournemouth, Ibrahimovic went into the match in fine form.
The Swede’s movement was significant in a United attack that looks far livelier than it did under the management of Louis van Gaal last season.
Intriguingly, Ibrahimovic appears to have bumped captain Wayne Rooney from penalty duties. He was quick to take on the responsibility when United were awarded a spot-kick; his finish was his 25th successful conversion from his last 28 attempts.
Pogba’s return to Old Trafford, four years after he left for Juventus without having made a Premier League start, has been eagerly awaited by United fans this summer.
His second debut for the club was delayed because of a suspension held over from his time in Italy but, with that served, manager Jose Mourinho tried to warn supporters against expecting too much too soon.
The midfielder is still getting back to full speed, having been given a break after helping France reach the Euro 2016 final – and that showed in his performance.
However, there was plenty of evidence to suggest that Mourinho was right to spend so much money to bring him back to Old Trafford. His display was a positive one, with more touches and more passes in the opposing half than any team-mate.
One surging run towards the end of the first half left four Southampton players in his wake, and demonstrated his power, while a second-half header from a Juan Mata corner flew just over the bar.
He did fade as the match reached its later stages – undoubtedly a result of the fact that he has not had a proper pre-season – but the Frenchman summoned up enough energy to blast a shot wide at the end of a late counter-attack.
A goal would have rounded off Pogba’s night perfectly, but he was happy enough. For him, victory was the perfect way to celebrate the 26th birthday of his brother, Partick Thistle striker Mathias Pogba.
Southampton’s Old Trafford run ends
Another summer has brought yet another squad overhaul at Southampton, with Sadio Mane, Graziano Pelle and Victor Wanyama all leaving the club, along with manager Ronald Koeman.
Claude Puel, Koeman’s replacement, is still finding his feet in the Premier League, and the same could be said of the reshaped squad he leads.
The visitors had their moments at Old Trafford, with Shane Long going close and Dusan Tadic seeing a goal ruled out for a push moments before Ibrahimovic’s decisive second.
Losing midfielder Oriol Romeu to an early injury did not help them, but having won 1-0 on each of their last two visits to Old Trafford, they rarely looked likely to extend that run.