Pep Guardiola got one over his old rival Jose Mourinho as Manchester City won a derby clash against Manchester United 2-1 to go three points clear at the top of the Premier League.
The victory on their rivals' home turf maintained City's 100 per cent start to the season and inflicted a first defeat on United.
City's Kevin de Bruyne was at his scintillating best and returned to haunt Mourinho, his former manager at Chelsea, by opening the scoring when he met a flicked header from Kelechi Iheanacho.
He then created City's second goal when his shot deflected off the post into Nigeria striker Iheanacho's path.
Zlatan Ibrahimovic reduced the deficit just before the break after City's new goalkeeper Claudio Bravo dropped a high cross, one of several errors during an unconvincing debut.
City held firm to wrap up the points and hand Guardiola first blood in the latest instalment of his simmering rivalry with Mourinho.
"We were the team trying to change the result," a defiant Mourinho told reporters. "We had the courage and the honesty and the dignity to go and chase with pride."
Arsenal enjoyed much of the possession against Southampton but lacked a cutting edge and needed Santi Cazorla's late penalty to take all three points after Jose Fonte was harshly penalised for tangling with Olivier Giroud.
"He did very well to score because he felt a heavy mental weight for the team," Arsene Wenger told reporters.
"It's a relief because we missed many chances and they had one or two opportunities having thrown everything forward."
Laurent Koscielny's overhead kick had earlier cancelled out Petr Cech's own goal.
Tottenham's Son Heung-min scored either side of halftime as Spurs rediscovered the fluid attacking football that made them such an irresistible offensive threat last season to outclass Stoke.
"What was most important was that we started a very difficult run of seven games in 20 matches with a win," said Spurs manager Mauricio Pochettino.
"It was the perfect result for us."
Two first-half goals from Michail Antonio put West Ham United in control against Watford, but the hosts drew level when Odion Ighalo and Troy Deeney hit a quickfire double at the end of the first half and Etienne Capoue and Jose Holebas completed a remarkable comeback with second-half strikes.
Crystal Palace got their first win of the season as they beat Middlesbrough 2-1, while Bournemouth beat West Bromwich Albion 1-0 and Burnley and Hull City drew 1-1.
In the late game, Roberto Firmino scored a double as Liverpool comfortably beat champions Leicester City at Anfield.