Championship Wrap: Burnley held by Cherries
After Tokelo Rantie had put the home side ahead six minutes after the break on Saturday, it looked as though Sean Dyche's men would be unable to reduce the deficit at the summit at all.
However, Keith Treacy tapped in after 67 minutes to extend their unbeaten league run to nine matches.
Ipswich Town also missed an ideal chance to put pressure on those in the play-off places as they were held to a goalless draw at home to Blackpool.
The stalemate keeps them in eighth place, two points off the top six, while Birmingham City's dismal home form continued as Lee Clarke suffered a 2-1 defeat against his former side Huddersfield Town.
Clark's side have won just once in their last 14 attempts at St Andrew's, with goals from Oliver Norwood and Adam Clayton ensuring Huddersfield ended a run of four straight away league defeats - Olly Lee's late goal proving merely a consolation for the hosts.
Nick Proschwitz was the hero for Barnsley in the South Yorkshire derby against Doncaster Rovers at the Keepmoat Stadium, scoring a minute from time to complete his brace and salvage a point for the visitors from a 2-2 draw.
The German, on loan from Hull City, put Barnsley ahead after 27 minutes before James Coppinger's double turned the game around - only for Proschwitz to snatch a draw for Danny Wilson's side late on.
Troy Deeney's second-half penalty was enough to give Watford a narrow 1-0 win over Middlesbrough in a game that saw Samba Diakite and Ben Gibson sent off to leave both sides with 10 men, while Millwall left it late to snatch a point from a 1-1 draw at home to fellow strugglers Bolton Wanderers.
Lukas Jutkiewicz put the visitors ahead after 15 minutes but Martyn Woolford fired home from a tight angle with eight minutes left to salvage a draw.