Meanwhile, Slaven Bilic became the first managerial casualty of the season as he was dismissed by West Bromich Albion. Former England boss Sam Allardyce has immediately been appointed as his successor.
At Anfield, Jurgen Klopp’s side took the lead through Mohamed Salah’s deflected strike in the first half of the eagerly-anticipated summit meeting.
Son Heung-min’s clinical strike drew Tottenham level before the interval as Jose Mourinho’s counter-attacking game-plan kept Liverpool in check.
But glaring misses from Tottenham forwards Steven Bergwijn and Harry Kane proved costly in the second half.
Firmino, who has found goals at Anfield so hard to come by, made them pay in the 90th minute when the forward headed home after escaping the attentions of Kane and Toby Alderweireld.
Klopp’s wild celebrations at full-time appeared to irk Mourinho, with the pair exchanging words before eventually seeming to make peace.
Liverpool are now three points clear of Tottenham after extending their unbeaten run to nine league matches with a result that showed they will not surrender the title without a fight.
The injury-ravaged Reds’ defiant display means they are unbeaten in 66 home league matches dating back to 2017.
Tottenham’s 11-game unbeaten run in the league came to an end in the most painful fashion.
But giving the champions a fright underlined their credentials as genuine title contenders.
Salah struck in the 28th minute when Curtis Jones drove into the penalty area and the ball broke to the Egyptian, whose shot looped up off Alderweireld and over Tottenham goalkeeper Hugo Lloris.
Son’s equaliser was a classic counter as he raced onto Giovani Lo Celso’s pass and drilled a confident low finish past Alisson Becker.
Liverpool refused to be subdued and Firmino’s thumping header from Andrew Robertson’s corner was a fitting coda to a pulsating encounter.
At the Emirates Stadium, defeat would have seen Arsenal lose five consecutive home league games for the first time in the club’s history as the pressure mounts on manager Mikel Arteta.
The Gunners could not have got off to a worse start as Theo Walcott opened the scoring on his return to the Emirates with a fine chipped finish over Bernd Leno from Che Adams’ pass.
Third-placed Southampton failed to build on their lead and were made to pay soon after the break as Arsenal scored just a third goal in their last nine league games and Pierre-Emerick Aubameyang’s first from open play since the first day of the season.
Bukayo Saka’s burst opened up the Saints defence and when Eddie Nketiah freed Aubameyang inside the area, the Arsenal captain curling an excellent finish into the far corner.
Arsenal’s joy was short-lived as they again found themselves a man down as Gabriel picked up two quick bookings.
“It’s very difficult to compete in this league when you play for so long with 10 men,” Arteta said.
“It makes it more complicated, but the boys stood up to it, they showed their character and resilience and they never gave up.”
Fifth-placed Everton won 2-0 at fourth-placed Leicester.
Richarlison opened the scoring thanks to an error from Kasper Schmeichel as the Leicester captain got a hand to the Brazilian’s effort from outside the box but could not keep it out.
Carlo Ancelotti’s men secured the points when Mason Holgate hammered home the rebound from point-blank range after Schmeichel nearly made amends with a brilliant stop from Dominic Calvert-Lewin.
Leeds won a seven-goal thriller against Newcastle 5-2 to move level on points with the Magpies, eight points clear of the relegation zone.
Fulham moved out of the relegation zone after a 0-0 draw with Brighton at Craven Cottage.
West Ham’s Sebastien Haller equalised with a superb overhead kick in a 1-1 draw against Crystal Palace, whose goalscorer Christian Benteke was sent off in the second half.
Baggies turn to Big Sam
Elsewhere former England boss Sam Allardyce returned to management for the first time in two-and-a-half years after being appointed as West Brom manager yesterday.
Allardyce, 66, takes over the Premier League strugglers after Slaven Bilic was sacked despite earning a 1-1 draw at Manchester City on Tuesday.
The Baggies are 19th in the table, but sit just two points off safety.
Allardyce has joined on an 18-month contract and will take charge for the first time in a Midlands derby against Aston Villa on Sunday.
“In Sam we have a man who has a proven Premier League pedigree with a track record of improving every club he has managed,” said Luke Dowling, West Brom’s sporting and technical director.
“We believe and, more importantly, Sam believes we have a group of players that have the quality needed to give the club its best chance of Premier League survival.”
Bilic led West Brom back to the top-flight in his only full season in charge, but paid for winning just one of the club’s first 13 Premier League games of the campaign.
The Croatian’s relationship with the club’s board had also soured in recent months after he was given little funding to bring in players in the close season.
“West Bromwich Albion have today parted company with Head Coach Slaven Bilic,” the club said in an earlier statement.
“Albion would like to thank Slaven and his coaching staff for their efforts in achieving promotion last season and wishes them all well in the future.”
Bilic is the first Premier League manager to be sacked in over a year as a three-month stoppage due to the coronavirus pandemic and empty stadiums since the return of English football has led to greater patience with coaches.
Allardyce has not been involved in a coaching role since leaving Everton in May 2018.
But he has a wealth of experience when it comes to keeping sides in the Premier League and now takes charge of a record eighth club in the English top-flight after previous spells at Bolton, West Ham, Newcastle Blackburn, Sunderland and Crystal Palace.