Summer signing Zlatan Ibrahimovic continued his goal-scoring run with the opening goal in the 36th minute after the ex-AC Milan striker guided a header past England goalkeeper Fraser Forster.
The 34-year-old towering striker added his second from the penalty spot after former Southampton left-back Luke Shaw was fouled inside the area in the second half.
And former United midfielder Giggs believes the new manager will be very pleased with the performance of his new signings against the Saints on Friday night.
“It wasn’t a totally dominant game from Manchester United,” Giggs told Sky Sports. “Southampton were always in the game.
“There were so many positives. Pogba’s performance, Ibrahimovic scoring twice, Shaw and Valencia with good performances.
“So a lot of positives.”
The Red Devils were 3-1 winners against Bournemouth in their opening Premier League game of the season last weekend thanks to goals from Juan Mata, Ibrahimovic and Wayne Rooney.
United are at the top of the Premier League table and three points clear of second-placed Liverpool following their comfortable win against the Saints.
The 20-time English champions will make the trip to promoted side Hull City at KC Stadium next Saturday 27 August.
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