Zlatan Ibrahimovic scored either side of half-time on his home debut as United made it two wins from two in the Premier League with an impressive win over Claude Puel's Saints.
The Swede headed home Wayne Rooney's cross nine minutes shy of the interval and then added a second from the spot shortly after the interval for his fourth goal in three games.
The win maintained the Reds 100% start to the new season under Mourinho and the manner and efficiency of the victory will fuel the belief- even at this early stage- that we can mount a genuine title challenge this time out.
United's world record signing Paul Pogba played the full 90 minutes in an eye-catching debut and went close to scoring on 13 minutes when he fired narrowly wide from Ibrahimovic's through ball.
Fraser Forster saved well from Rooney, Shane Long should have done better when clean through and Dusan Tadic shot off target before Southampton were forced into an early change after Oriol Romeu was forced off with an injury.
Rooney and Zlatan had set Jose Mourinho's side on their way in our opener at Bournemouth last weekend, and linked up again to deadly effect as the skipper picked out Ibrahimovic to thump home a brilliant header from close range on 36 minutes.
Juan Mata blazed over the bar and Tadic had a goal disallowed before Anthony Martial forced a fine save from Forster with a 20 yarder shortly after the resumption.
It did not take long for the hosts to stretch their advantage as former Southampton man Luke Shaw went down under a challenge from Saints substitute Jordy Clasie and Ibrahimovic clinically dispatched the resultant spot-kick.
Pogba had displayed his full repertoire of attributes- strength, vision and creativity- and almost added a dream goal to his impressive debut when he went close with a header from a Mata pass.
Armenia captain Henrikh Mkhitaryan was introduced with 15 minutes remaining in place of the Spaniard before Martial was replaced by Ander Herrera as Mourinho looked to consolidate the victory in the professional manner that his teams have become known for.
Pogba went close with a drive from distance in injury time, but despite not getting on the scoresheet the 23-year-old Frenchman's industrious display in midfield hinted at what we hope will become a stellar, second Old Trafford career.
United Faithful Man of the Match: With an honourable mention to Pogba who impressed on his return to the club, Zlatan again proved to be our matchwinner, already looks an inspired signing.