Carlo Ancelotti and Mikel Arteta got their Everton and Arsenal tenures under way as Liverpool continued their march towards the title.
Liverpool thrashed second-placed Leicester City 4-0 to extend their lead at the top of the Premier League to 13 points with a game in hand.
Club World Cup hero Roberto Firmino scored either side of a James Milner penalty and Trent Alexander-Arnold capped a phenomenal display by completing the scoring at the King Power Stadium.
Manchester United were also big winners, coming from behind to beat Newcastle United 4-1 at Old Trafford, while elsewhere in the Premier League two keenly anticipated managerial tenures got under way.
Carlo Ancelotti saw Dominic Calvert-Lewin head Everton to a 1-0 win over Burnley in his first game in charge at Goodison Park, while Mikel Arteta had Pierre-Emerick Aubameyang to thank for salvaging a 1-1 draw for Arsenal at Bournemouth.
Yet the result of the afternoon came at Chelsea, where superb goals from Michael Obafemi and Nathan Redmond meant Frank Lampard's men were unable to build upon their impressive triumph at Tottenham last time out.
Spurs moved back to within three points of fourth-placed Chelsea after coming from behind to beat Brighton and Hove Albion 2-1, a result repeated in the south of the capital as Crystal Palace stole the points against West Ham courtesy of a fabulous Jordan Ayew solo effort.
Watford's 1-1 draw at Sheffield United lifted them off the bottom of the table, with Norwich City now propping up the rest after going down 1-0 at Aston Villa.
No sign of home comforts for Lampard, but better news for Solskjaer
Leicester's designs on a title push have been checked by defeats to Manchester City and now Liverpool, who have won 17 of their 18 Premier League games this season.
They last lost in the competition on January 3 and Alexander-Arnold, who set up both of Firmino's goals, gave an awesome demonstration of the quality at their disposal.
By contrast, Chelsea have now lost five of their past seven Premier League games and three out of four at Stamford Bridge after Southampton were able to toast an unlikely hero.
Obafemi got his chance up front as top scorer Danny Ings was rested and he drove at a backpedalling Blues backline to finish emphatically after the half hour. Redmond capped a fine team move 17 minutes from time.
Spurs were facing a fresh setback in their game against Brighton when Adam Webster powered in Pascal Gross' free-kick, but Harry Kane continued his habit of finding the net on Boxing Day and Dele Alli maintained his prolific form under Jose Mourinho with a 72nd-minute winner.
Ole Gunnar Solskjaer watched his Manchester United turn on the style after going behind to an early Matty Longstaff goal against Newcastle.
As memories of a painful 1-0 defeat to the Magpies in October came flooding back, the hosts found an extra gear at Old Trafford to turn the match around, with Martial, Greenwood and Rashford showing a clinical touch.
Encouraging early signs for Ancelotti and Arteta
Burnley created little at Goodison Park but Everton had to be patient before the breakthrough arrived with 10 minutes to play.
Djibril Sidibe's searching cross found a diving Calvert-Lewin, who headed home via the post.
The Clarets are now below 11th-placed Arsenal on goal difference after Arteta got a first-hand look at some of his club's long-standing defensive problems,
Dan Gosling put Bournemouth ahead after the Gunners were carved apart down the right but the Gunners summoned a battling response and Aubameyang turned in his 12th Premier League goal of the season.
Ayew sends Eagles soaring
Palace had a day to remember against West Ham despite falling behind to a Robert Snodgrass goal at Selhurst Park.
Cheikhou Kouyate stole in to equalise against his former club before Ayew danced through a succession of challenges and found a delightful chipped finish in the final minute.
West Ham are a point and a place above the relegation zone after third-bottom Villa saw off fellow strugglers Norwich.
Substitute Conor Hourihane swept in Jack Grealish's pass eight minutes after coming on, while Tom Heaton excelled in the home goal.
Watford made it back-to-back draws under Nigel Pearson, leading briefly at Bramall Lane through Gerard Deulofeu before Oliver Norwood levelled from the penalty spot.