Arsene Wenger's side did not have to be at their best to overcome an organised Burnley, who stay second from bottom in the table, but scored early through Aaron Ramsey and then eased through largely unthreatened.
While Chelsea, who play Queens Park Rangers on Sunday, have two games in hand, Wenger's side host the leaders in two weeks.
At the other end of the table, Aston Villa took another step towards safety after Christian Benteke's goal secured a 1-0 win over Tottenham Hotspur as manager Tim Sherwood enjoyed a winning return to his former club.
Villa, who moved up to 15th on 32 points, are six clear of the relegation zone.
They are a place and three points above Sunderland, whose own battle to avoid the drop suffered in a stinging 4-1 home defeat by Crystal Palace with Yannick Bolasie completing a 12-minute hat-trick for the visitors.
The relegation battle remains a congested dogfight with bottom club Leicester City continuing their escape bid with a 3-2 victory over West Bromwich Albion as Hull City missed the chance to put clear water between themselves and danger.
Hull lost 2-0 to Southampton to stay 17th, while Ronald Koeman's side moved up to fifth on 56 points, above Liverpool and five behind fourth-placed Manchester City, who take on local rivals Manchester United at Old Trafford on Sunday.
Stoke City's Marko Arnautovic scored in the 90th minute to snatch a 1-1 draw with West Ham United and Swansea City equalled their highest ever points tally (47) in a Premier League season following a 1-1 draw with Everton.
