Spurs' next three games, meanwhile, are against Swansea, Watford, and Bournemouth - all of whom are still not clear of relegation trouble.
"It adds a bit more pressure," Chelsea captain Gary Cahill said.
It was only a fourth league loss this season for Chelsea, and first since the 2-0 defeat at Tottenham on Jan. 4. Chelsea had won its previous 10 home league matches stretching back to October.
Here's a closer look at Saturday's games, during which Liverpool maintained its recent dominance of the Merseyside derby and Manchester United endured more frustration at Old Trafford:
CHELSEA 1, CRYSTAL PALACE 2
The implications of this result to the title race will overshadow the fact that Palace has won four straight games to boost its bid to stay in the Premier League.
Wilfried Zaha spearheaded Palace's daring attacking display, canceling out Cesc Fabregas's fifth-minute opener before setting up striker Christian Benteke for the winner moments later. All three goals were scored in the first 11 minutes and it was a lovely finish from Benteke, who calmly lifted the ball over the advancing Thibaut Courtois at the end of a counterattack.
Despite its improved form, Palace is still just four points clear of the relegation zone with nine games left, with many of its rivals having also started to pick up points.
BURNLEY 0, TOTTENHAM 2
Eric Dier and substitute Heung-min Son scored second-half goals for Tottenham, which earned a fourth straight league win.
Last season, Spurs were chasing Leicester to the Premier League trophy only to falter in the final stages. That experience could prove vital.
"We have to be there if Chelsea fail," Tottenham manager Mauricio Pochettino said, "and we are there. We are fighting for the Premier League."
There were some negatives for Spurs, who lost center midfielders Victor Wanyama and Harry Winks to injuries.
MANCHESTER UNITED 0, WEST BROMWICH ALBION 0
Winning the Europa League may offer United its best chance of a Champions League return after this latest setback at home.
West Brom was the eighth side to leave Old Trafford with a draw this campaign, joining the likes of Hull, Stoke, and Burnley in defying injury-hit United.
United stayed fifth and was four points behind Manchester City - the occupier of the final Champions League qualification place - having played the same number of games.
LIVERPOOL 3, EVERTON 1
It's now 13 Merseyside derbies in the league without defeat for Liverpool dating to October 2010 - equaling a club record - and this latest win was inspired by Brazil playmaker Philippe Coutinho, who scored one goal after a weaving run and also set up substitute Divock Origi for the clinching third.
Liverpool hired a private jet to get Coutinho back from international duty in good time for the match and it proved to be a worthwhile investment.
Winger Sadio Mane scored the opening goal for Liverpool in the eighth minute but limped off with a left leg injury in the 57th after landing awkwardly in a challenge. Liverpool already has attacking midfielder Adam Lallana out injured.
Liverpool moved above Manchester City into third place.
OTHER RESULTS
Leicester's revival continued under manager Craig Shakespeare as Wilfred Ndidi and Jamie Vardy handed the champions a 2-0 victory over Stoke. Shakespeare, who replaced title-winning manager Claudio Ranieri, joined Guus Hiddink, Jose Mourinho, Pep Guardiola, and Carlo Ancelotti in winning his first four Premier League games in charge.
Last-place Sunderland dropped seven points adrift of safety by losing 1-0 at Watford and third-to-last Hull rallied to beat West Ham 2-1, moving into a tied on points with Swansea.
Bournemouth midfielder Harry Arter blazed a late penalty over the bar in a 0-0 draw at Southampton.
