Alexis Sanchez struck two minutes from time to give Arsenal victory just as it looked like Southampton would hold out for a draw at The Emirates.
Visiting Spurs goalkeeper Fraser Forster had kept Arsenal at bay with a collection of fine saves from Danny Welbeck and substitute Olivier Giroud, but he was powerless to prevent Gunners talisman Sanchez pouncing on Aaron Ramsey’s cross to score his 14th goal of the season.
Arsene Wenger’s side deserved the win after applying intense late pressure but Southampton were forced to play out the crucial final minutes without defender Toby Alderweireld, who suffered a hamstring injury after manager Ronald Koeman had used his three substitutes.
The victory, coming on the heels of the win at West Bromwich Albion on Saturday, pushes Arsenal into the top six, while Saints stay third despite a second successive defeat following their home loss against Premier League champions Manchester City on Sunday.
A small group of Arsenal fans brandished a banner at The Hawthorns calling for Wenger to quit, but they can be grateful that he has brought such a gem as the Chilean Sanchez to north London.
At Stamford Bridge, Didier Drogba inspired Chelsea to a win over Tottenham to maintain the Blues’ six-point lead at the top of the table.
Tottenham missed two good chances early on – Harry Kane hitting the bar then dragging a shot wide – and Chelsea went ahead when Eden Hazard finished sweetly following a one-two with Drogba.
The striker, who replaced the suspended Diego Costa, then netted with a low shot following a Hugo Lloris mistake.
Substitute Loic Remy completed the win with a smart finish from 12 yards.
There was plenty to admire about Chelsea, who once again turned on the style for 10 first-half minutes to blow away their second-best opponents.
Tottenham, who are still without a win at Stamford Bridge since 1990, could not deal with the sublime skill of Hazard, the power and physicality of Drogba and the rampaging runs down the right from full-back Branislav Ivanovic.
And Sergio Aguero took his Premier League goal tally to 14 with a double as Manchester City overcame Sunderland to make it three straight top-flight wins.
Sunderland went ahead when Connor Wickham fired past Joe Hart while under pressure from Pablo Zabaleta.
But Argentina forward Aguero equalised with a fierce 16-yard finish before Stevan Jovetic fired through former City keeper Costel Pantilimon’s legs.
Zabaleta increased the lead with a fine chip before Aguero completed the rout.
City’s performance was every bit as convincing as the scoreline suggests, with Manuel Pellegrini’s side rejuvenated as they head towards the festive programme with growing belief, reports the BBC.
And Hull ended a run of four consecutive league defeats thanks to Sone Aluko’s second-half equaliser at Everton.
Substitute Aluko twisted and turned defender Sylvain Distin before firing a low, angled shot past Tim Howard.
Everton took the lead when Romelu Lukaku fired in his sixth of the season from Kevin Mirallas’ pull-back.
Arsenal 1-0 Southampton
Chelsea 3-0 Tottenham
Everton 1-1 Hull
Sunderland 1-4 Man City