Wayne Rooney suffered a third straight defeat since taking the hot seat at Birmingham on Saturday as Championship leaders Leicester made it 13 wins from 14 matches.
Southampton took the lead against Birmingham when Taylor Harwood-Bellis headed home in the ninth minute and doubled their advantage midway through the first period through Carlos Alcaraz.
Substitute Jay Stansfield narrowed the deficit moments after his 57th-minute introduction but Southampton made sure of the three points in the 86th minute when Adam Armstrong scored his eighth goal of the season.
Rooney, who returned to English football earlier this month from the United States, had been booed after Wednesday's 2-0 home defeat by Hull, and Saints supporters chanted "sacked in the morning" at the Manchester United and England great.
Birmingham fans supported their manager with cries of "Rooney, Rooney" and "Wayne Rooney's Blue Army".
"I'm obviously disappointed we've lost but there were a lot more positives today," Rooney told the BBC.
"I told the lads before the game Southampton are the best in the league with the ball so we knew they'd have it quite a bit, and our organisation and shape was important. We did that well.
"In the second half we were better. I wanted us to play more in their half and pin them in, and we did that at times. But the goals we gave away were sloppy goals. Those details need to improve."
Harry Winks's late goal gave Leicester a 2-1 victory over 10-man QPR and maintained their five-point lead at the top of the Championship.
Stephy Mavididi opened the scoring and Andre Dozzell equalised for QPR shortly before the interval, but Dozzell was sent off shortly before the hour mark.
Struggling QPR battled hard, but the Foxes eventually made their numerical advantage count in the 80th minute.
Second-placed Ipswich came from a goal down to stretch their unbeaten Championship run to nine games with a 3-2 victory over Plymouth.
Marcus Harness struck in the 86th minute to put the game beyond Argyle, despite a late reply from Joe Edwards.
Leeds hammered Huddersfield 4-1 at Elland Road to keep their bid for a return to the Premier League on track.
Dan James and Crysencio Summerville both hit first-half doubles as Daniel Farke's men finally produced the free-scoring display their dominance at home has threatened all season.