Manchester United moved into the top four of the Premier League with a last second goal from Marcus Rashford earning them a 1-0 win over West Ham United at Old Trafford.
Everton began life after Rafa Benitez in much the same manner as they ended it -- in defeat -- a 1-0 loss at home to Aston Villa leaving them in 16th place, just four points above the relegation zone.
Newcastle United claimed only their second league win of the season as they beat Leeds United 1-0 away, boosting their hopes of beating the drop.
Wolverhampton Wanderers won 2-1 at Brentford where the match was halted because of a drone flying above the ground.
City were stunned after seven minutes at St Mary's as Kyle Walker-Peters struck his first Premier League goal, a stunning effort with the outside of his right foot.
It knocked Pep Guardiola's side out of their silky stride and it took a 65th-minute header by Aymeric Laporte to earn them a second draw of the season against Southampton.
Kevin de Bruyne, Gabriel Jesus and Rodri all hit the woodwork for City as they extended their lead at the top to 12 points, although second-placed Liverpool have played two games less. Liverpool face Crystal Palace on Sunday.
"I don't understand the way people say that now, after this result, the race is open, when before it is over," Guardiola, whose side have 57 points, said.
"I would love to be 40 points ahead of Liverpool and Chelsea, but that's impossible. I would never expect to be in this position, with this margin."
United's title aspirations have long been over and their target is now finishing in the top four.
They created little against a cautious West Ham but interim manager Ralf Rangnick threw on Rashford, Edinson Cavani and Anthony Martial and they finally got their reward.
Martial collected from Cristiano Ronaldo and fed Cavani who slipped a low ball across for Rashford to score.
The three points pushed United above West Ham and back in the top four for the first time since early October.
There was an unpleasant atmosphere at Goodison Park where visitors Aston Villa had players hit by missiles thrown from the crowd.
Emiliano Buendia scored the decisive goal, just before halftime, with a header that looped over keeper Jordan Pickford and the celebrations led to a bottle being launched from the stands and hitting the Villa players.
Lucas Digne, who was booed by Everton fans on his return to Goodison Park since last week's transfer, provided the assist and he was also hit by an object, with stewards and police trying to identify the perpetrators.
Everton, who are searching for a new manager and had ex-striker Duncan Ferguson in charge on a caretaker basis, have won only once in the league since September.
Jonjo Shelvey's 75th minute goal earned Newcastle a vital win at Leeds, moving them to 18th in the standings, one point from the safety zone, having played one game fewer than Norwich City in 17th, and seven points behind Leeds in 15th.
"It was a massive win for us," manager Eddie Howe said. "We hope to use it as a turning point in our season, we need to."
Wolves midfielder Ruben Neves struck in the 78th minute to seal a 2-1 win at Brentford although the main talking point was a 19-minute delay caused by a drone.
Joao Moutinho's opener had been cancelled out by Brentford's Ivan Toney.
Sunday's big game takes place at
Stamford Bridge where third-placed Chelsea face sixth-placed Tottenham Hotspur.