The unlikely reverse, which Conte admitted made the title race "more interesting" for everyone, left Chelsea on 69 points with Spurs having moved on to 62 and Liverpool on to 59, though the Reds have played a game more than the top two.
Such has been Chelsea's dominance at the Bridge this season that once Cesc Fabregas had put them ahead after just five minutes, it all promised to be plain sailing towards an 11th straight home win in the league for the Blues.
Yet two splendid goals from Wilfried Zaha and Christian Benteke in the space of three minutes soon after changed the complexion of the game with Palace then defending stoically to earn the unlikeliest of wins.
Spurs had appeared to be labouring at Turf Moor without injured striker Harry Kane and they lost Victor Wanyama and Harry Winks -- the latter to what appeared a serious ankle injury -- before the interval.
Yet Eric Dier and Son Heung-min struck in the second half to earn the points, leaving an encouraged Spurs manager Mauricio Pochettino to declare: "It was important for us to be there if Chelsea failed -- and we are there. We're there fighting for the Premier League."
With Chelsea on Wednesday next facing Manchester City, who currently lie fourth on 57 points and who first face Arsenal on Sunday, it is little wonder that the Blues' defeat has put a new spring in Pochettino's step.
Juergen Klopp will feel invigorated too after becoming the first Liverpool manager to win his first three Merseyside derbies as his side won with goals from Sadio Mane, the inspired Philippe Coutinho and Divock Origi.
Liverpool made it 17 league matches unbeaten at Anfield against their city rivals after Mane's brilliant early individual effort was answered by a first goal for Everton from Matthew Pennington.
The youngster, though, was bamboozled less than three minutes later by the skill of Coutinho, who curled a delightful shot into the corner before sealing his masterful display by putting in substitute Origi.
KOEMAN CRITICAL
Everton boss Ronald Koeman later criticised Klopp and the Liverpool bench for their "crazy" response to a bad tackle from Ross Barkley on Dejan Lovren.
"Tackles are part of football...we don't make a show from the bench like Liverpool," Koeman told Sky Sports.
"I don't like coaches from the bench the whole time shouting to referees and linesmen, making a big show about tackles."
Jose Mourinho was left in a grumpy mood again after his toothless Manchester United, while extending their unbeaten league sequence to 19 matches, slipped up in the race for Champions League places, held to a goalless draw at Old Trafford by West Bromwich Albion.
It was United's 11th draw, which leaves them in fifth place on 53 points.
At the other end of the table, Sunderland's plight is looking increasingly dire following another defeat, with Miguel Britos heading his first goal for Watford in the 1-0 win at Vicarage Road.
Hull City came from behind to beat West Ham United 2-1 with Andrea Ranocchia notching the Tigers' 85th-minute clincher, moving them up to 27 points in 18th place while Sunderland are rooted on 20.
Craig Shakespeare's extraordinary start to management at Leicester City continued as the champions beat Stoke City 2-0 with goals from Wilfred Ndidi and Jamie Vardy.
Victory meant that Shakespeare has become the first British manager ever to win his first four top-flight league games in the Premier League era.
(Reporting by Ian Chadband; Editing by Toby Davis)
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