England striker also becomes the top scorer of 2017 across Europe with his hat-trick, edging ahead of Barcelona's Messi.
Morata fires Chelsea to victory, Liverpool thrash Swansea, Kane breaks Shearer record: Premier League round-up
Tottenham Hotspur's Harry Kane became Europe's most prolific striker of 2017 with a second hat-trick in four days to break a 22-year-old Premier League record as his side thumped Southampton 5-2 on Tuesday.
Jesse Lingard struck twice, the second in stoppage time, as Manchester United hit back from two goals to draw 2-2 with Burnley and deny the visitors a first win at Old Trafford since 1962.
Second-placed United's second consecutive 2-2 draw allowed Chelsea to close to within a point of Jose Mourinho's side with a 2-0 home victory over Brighton and Hove Albion.
Liverpool were at their attacking best to pile more misery on bottom club Swansea City, running out 5-0 winners at Anfield. Philippe Coutinho opened the scoring before two goals from Roberto Firmino, whose second came moments after Trent Alexander-Arnold doubled Liverpool's advantage. Alex Oxlade-Chamberlain then got his first goal for the club with eight minutes remaining.
There was no doubt who the spotlight was on though as England striker Kane eclipsed Alan Shearer's record 36 Premier League goals in a calendar year, taking his tally to 39 in 2017 and 18 this season with another finishing masterclass.
Two close-range efforts and a superb dinked finish took his tally in all competitions in the calendar year for club and country to 56, lifting him ahead of Lionel Messi who hit 54 for Barcelona and Argentina.
Kane is the first player apart from Cristiano Ronaldo and Messi to finish the year as top scorer in Europe since 2009.
With runaway leaders Manchester City not in action it was a chance for United to close the gap to 10 points but they ended the day 12 behind as Burnley came close to a shock.
Ashley Barnes gave Burnley a third-minute lead and the visitors went further ahead when Belgian midfielder Steven Defour curled a 36th-minute free kick past David De Gea.
Mourinho put Lingard on in the second half in place of Zlatan Ibrahimovic and, after missing a sitter, he reduced the arrears with a back-heel flick. Burnley hung on desperately but Lingard drove home the equaliser in stoppage time.
Chelsea were frustrated in the opening half at Stamford Bridge but Alvaro Morata and Spanish compatriot Marcos Alonso scored after the break to earn the three points and move Chelsea to 42 points from 20 games. Tottenham have 37.
A fierce relegation battle on the south coast saw Bournemouth snatch a point at the death with a 3-3 draw against West Ham United - Callum Wilson's controversial goal denying the visitors a crucial victory.
Wilson's effort, after Marko Arnautovic's two late goals had the turned the game on its head to give West Ham a 3-2 lead, was initially disallowed for offisde but was finally allowed to stand by referee Bobby Madley.
"The mistake was the referee went to the linesman. He knows he made a mistake, but we all make mistakes," Arnautovic said.
The result left Bournemouth third from bottom, a point and a place below West Ham.
Watford snapped a four-game losing streak as as they came back to beat Leicester City 2-1 thanks to an own goal by Leicester keeper Kasper Schmeichel.
Huddersfield Town drew 1-1 at home to Stoke City and second-bottom West Bromwich Albion did little to ease their relegation fears as they drew 0-0 at home to Everton.