Tottenham 5-2 Southampton
Bournemouth 3-3 West Ham
Chelsea 2-0 Brighton
Huddersfield 1-1 Stoke
Manchester United 2-2 Burnley
Watford 2-1 Leicester
West Brom 0-0 Everton
Liverpool 5-0 Swansea
Bournemouth and West Ham both let two points slip away, but Brighton, WBA, Huddersfield, Swansea and Stoke did no better. So Newcastle saw out a good day as the prepared for Man City.
Philippe Coutinho provided the style and compatriot Roberto Firmino the substance as Liverpool's brilliant Brazilians dispatched rudderless Swansea 5-0 in clinical fashion at Anfield.
Things looked bleak for the Premier League's bottom side, still searching for their next manager after sacking Paul Clement last Wednesday, when Coutinho curled home a superb sixth-minute opener.
The hosts' sluggishness prevented Jurgen Klopp's scoring further until early in the second half when Firmino volleyed in Coutinho's free-kick before adding his second after Trent Alexander-Arnold drilled in a half-volley off the underside of the crossbar, with Alex Oxlade-Chamberlain firing in the fifth seven minutes from time.
It allowed Liverpool to regain fourth place after Tottenham's victory earlier in the day but left Swansea five points from safety after a seventh successive away defeat.
Substitute Jesse Lingard came to Manchester United's rescue as his second-half double secured a 2-2 Boxing Day draw with Burnley at Old Trafford.
The stadium was left stunned in the first half as the Clarets claimed a 2-0 lead via Ashley Barnes' close-range finish in the third minute and Steven Defour's superb strike in the 36th.
Having come on for Zlatan Ibrahimovic at the interval, Lingard then pulled a goal back eight minutes after the break with a back-heel before striking an equaliser in stoppage time.
Second-placed United are now 12 points behind Premier League leaders Manchester City - who visit Newcastle on Wednesday - having played a game more, while Burnley remain seventh.
Third-placed Chelsea are a point behind United after the champions defeated Brighton 2-0 at Stamford Bridge.
Alvaro Morata registered his 10th league goal of the season with a header in the opening minute of the second half and Marcos Alonso added another on the hour mark.
Harry Kane broke Alan Shearer's Premier League record for goals scored in a calendar year by hitting a hat-trick in Tottenham's 5-2 victory over Southampton.
Kane needed only one goal to pass the 36 scored by Shearer in 1995 but the Spurs striker banged in three at Wembley to finish 2017 on an astonishing 39 goals in 36 league matches.
Dele Alli and Son Heung-min helped put Southampton out of sight in the second half despite Sofiane Boufal pulling one back at 4-0 and substitute Dusan Tadic reducing the deficit late on.
But while five different scorers made for a frenetic, if undoubtedly one-sided contest, Kane was the star of the show from the moment he headed past Saints goalkeeper Fraser Forster in the 22nd minute.
Kane now has 18 goals, three more than Mohamed Salah, who sits second in the race. Sergio Aguero and Raheem Sterling follow with 12 each.
Bournemouth and West Ham remain 18th and 17th respectively, a point apart, after they played out a thrilling 3-3 draw at the Vitality Stadium.
The Cherries bounced back from James Collins' early header with goals from Dan Gosling and Nathan Ake, and Marko Arnautovic then netted twice to put the Hammers 3-2 up before a controversial equaliser in stoppage time ensured it finished honours even.
Callum Wilson was credited with the hosts' third after he had the final touch as Ake headed goalwards. There was a suspicion of both handball and offside, but referee Bobby Madley eventually awarded the goal after a lengthy conversation with assistant Simon Long.
Watford halted their four-game losing streak as they came from behind to beat Leicester 2-1 at Vicarage Road.
After Riyad Mahrez put the Foxes in front, an effort from Molla Wague - who had a spell on loan at Leicester last season - and a Kasper Schmeichel own goal turned the contest around.
Elsewhere, Huddersfield were held to a 1-1 draw at home by Stoke, who levelled through Ramadan Sobhi after Tom Ince's 10th-minute goal, while 19th-placed West Brom and Everton drew 0-0 at The Hawthorns.