Defending champion City was frustrated in the first half at St. Mary's, but Yaya Toure, Frank Lampard and Gael Clichy netted to claim a 3-0 victory. The last two goals came with City down to 10 men following Eliaquim Mangala's 74th-minute dismissal.
"We knew what we were coming up against today, a very good team in very good form," Lampard said. "I think you could see from the outset today that our attitude was absolutely bang on."
With Arsenal and Manchester United up next, this was a disappointing start to a sequence of games that will show how realistic Southampton's top-four ambitions are.
Tottenham, led by former Southampton manager Mauricio Pochettino, is just two points from the Champions League places after beating Everton. Goals from Roberto Soldado and Christian Eriksen scored saw Tottenham come from behind to win 2-1 for the third time in four league games.
Chelsea ends the weekend with its lead cut to six points after failing to score for the first time this season in Saturday's 0-0 draw at Sunderland.
City faced similar frustration on the south coast until six minutes into the second half when Sergio Aguero drifted into Southampton's penalty area and laid the ball off for Toure to fire a low, deflected shot into the net.
When Mangala was shown a second yellow card for barging over Shane Long, having already been booked for fouling Dusan Tadic, it appeared Southampton could have a route back into the game.
City had other ideas, exploiting Southampton's push for an equalizer by launching a counterattack through James Milner, who set up Lampard to score from the edge of the area in the 80th.
City wasn't finished. Aguero raced down the left flank before teeing up Clichy to score his first league goal for the club in the 88th and condemn Southampton to its first home loss of the season.
"That was not good enough from us, and we got punished for that," Southampton manager Ronald Koeman said.
At White Hart Lane, Soldado clinched Tottenham's win with his first league goal since March — a barren run lasting 593 minutes.
The Spain striker fired in the winner in first-half stoppage time after being released by Aaron Lennon.
"It hasn't been easy," Tottenham manager Mauricio Pochettino said. "It's always frustrating for a striker when he doesn't score ... he's (been) feeling the pressure."
Soldado had played a part in Everton's opener, failing to prevent Kevin Mirallas curling the ball from the edge of the area into the roof of the net in the 15th minute.
Tottenham's equalizer came six minutes later when Harry Kane, a constant threat for the hosts, had a shot parried by goalkeeper Tim Howard, and Eriksen responded by netting from a tight angle.
Spurs climbed three places to seventh, leaving Everton in 10th.