Diego Costa fired his 10th goal of the season as Chelsea maintained their four-point lead at the top of the Barclays Premier League with a 2-1 win over Liverpool at Anfield.

Costa polished off a Cesar Azpilicueta cross in the 67th minute as Jose Mourinho's men fought back from the shock of conceding an eighth minute opener to Emre Can.

Costa's effort appeared to have sealed victory but Chelsea still had to ride their luck when a Gary Cahill handball in the box went unpunished.

Substitute Shane Long struck twice late on as second-placed Southampton stayed within touching distance of the leaders with a 2-0 win over Leicester at St Mary's. Long replaced Sadio Mane in the 67th minute and curled home a fine opener eight minutes later, before beating the visitors' offside trap to stroke home his second with 10 minutes to go.

Louis Van Gaal was a relieved man after watching his Manchester United side labour to a 1-0 win over Crystal Palace at Old Trafford.

United's defensive frailties were again laid bare, but the good luck gods were with United who grabbed the winner in the 67th minute when substitute Juan Mata played a neat one-two with Angel di Maria before firing home.

Burnley claimed their first top-flight win at the 11th time of trying as they edged a 1-0 win over Hull at Turf Moor.

Recalled Ashley Barnes was the hero as he headed home Kieran Trippier's 50th minute cross to finally get Sean Dyche's season up and running.

West Ham were frustrated by a resolute Aston Villa side who were looking to end a miserable run of six successive defeats and who clung on for a goalless draw.