Liverpool cut Manchester City's lead at the top of the Premier League to a single point on Sunday as Manchester United slipped to their first domestic defeat under Ole Gunnar Solskjaer at Arsenal.
Chelsea, also in the hunt for the Champions League qualification spots, needed a last-gasp equaliser from Eden Hazard to earn 1-1 draw against Wolves.
A disappointing run of results has badly dented Liverpool's bid for a first English league title since 1990 and fans' nerves were jangling after they fell behind against struggling Burnley at Anfield on Sunday.
But Roberto Firmino and Sadio Mane both scored twice as Jurgen Klopp's team battled back to win 4-2, lifting them to 73 points, one behind Pep Guardiola's City, who saw off Watford on Saturday.
"The message from today is that nobody gets rid of us," said a defiant Klopp, whose team had won just two of their previous six Premier League matches. "We had the perfect mixture of fighting the opponent and playing football.
"All we have to do is make sure that we stay in this really interesting competition on top of the table. We have no problem with confidence, we're in a good moment."
Tottenham's third defeat in four Premier League matches on Saturday has thrown the race for the top four -- the passport to the Champions League -- wide open.
United travelled to the Emirates Stadium brimming with confidence after their astonishing Champions League comeback against Paris Saint-Germain in midweek.
Solskjaer had won 13 and drawn two of his previous 15 league and cup fixtures since succeeding the sacked Jose Mourinho in mid-December but they fell behind in the 12th minute.
- Champions League race -
Granit Xhaka's strike from distance swerved through the air to wrong-foot United goalkeeper David De Gea.
Both teams went close thereafter, with Fred hitting a post and Romelu Lukaku guilty of wasting some gilt-edged chances but the home side doubled their lead midway through the second half when Pierre-Emerick Aubameyang scored from the penalty spot after Fred was penalised for bringing down Alexandre Lacazette.
Arsenal's 2-0 victory lifted Unai Emery's side into fourth, just one point behind north London rivals Spurs and meant they leapfrogged United in the process as they target a return to the Champions League after two seasons away from Europe's top club competition.
"We created so many more chances today than when we beat them in the FA Cup," said Solskjaer. "Sometimes it happens, we hit the woodwork twice and had five very big chances ourselves. The referee will be disappointed when he sees it as I don't think it is a penalty.
"We just had to go for it towards the end, but we were not really at it and it is one of those days where you have to dust yourselves down from."
The win was soured by an incident in which a fan ran onto the pitch and appeared to bump into Chris Smalling after the spot-kick -- it followed an incident in the earlier Championship game, when Aston Villa captain Jack Grealish was punched by a pitch invader during the match against Birmingham.
Earlier, Hazard came to Chelsea's rescue in injury time, firing in from long range to grab a point against Wolves at Stamford Bridge.
Chelsea enjoyed the bulk of the possession but Wolves took the lead through Raul Jimenez in the 56th minute with their first shot on goal after an incisive counter-attack and looked on track for an impressive win until Hazard struck.
Chelsea remain in sixth place, on 57 points, but manager Maurizio Sarri is confident his team can secure Champions League qualification.
City beat Watford 3-1 on Saturday thanks to Raheem Sterling's 13-minute hat-trick but Spurs, on the fringes of the title race just two weeks ago, slumped to their third Premier League defeat in just four games against Southampton.
There were also wins on Saturday for Brighton, Cardiff, Bournemouth, Leicester and Newcastle.