Crystal Palace moved six points clear of the relegation zone with victory over Brighton, Huddersfield also boosted their survival chances with a 1-0 win against Watford and Everton were held to a 1-1 draw by Swansea at the Liberty Stadium.
Here are some of the day's best Premier League stats:
- Chelsea's Olivier Giroud has now scored 19 Premier League goals as a substitute after netting two in eight minutes when he came on against Southampton. Bournemouth striker Jermain Defoe, with 24, is the only player to have scored more.
- The Blues won a Premier League game from two goals down for the first time since August 2002, when they beat Charlton Athletic 3-2 under Claudio Ranieri.
- Burnley have won five consecutive matches in the top flight for the first time since November 1968.
- Leicester striker Jamie Vardy has been on the losing side in eight games this season when he has scored - a record for a single Premier League campaign.
- Crystal Palace's 3-2 victory over Brighton saw five goals scored in the first half, which is the most in the league this season.
- Palace forward Wilfried Zaha netted his first headed league goal and scored twice in the same Premier League match for the first time.
- Watford have picked up one point from a possible 30 away from home since December.
- Huddersfield have won two of their past four league games at home after failing to win any of the previous five.
- Swansea have conceded 13 own goals in the Premier League since 2014-15 - five more than any other side.
- Since keeping two clean sheets in December, Everton have conceded in their past seven Premier League games on the road.