Matt Tubbs scored his first goal since joining Bournemouth from Crawley as they beat Exeter with two late goals.
Richard Logan went close to putting the visitors in front but his header was well saved by Darryl Flahavan.
Tubbs opened the scoring in the second half when he fired in substitute Scott Malone's cross from six yards.
Malone added a second soon after, breaking away from an Exeter corner before laying the ball to Tubbs, who then picked him out at the far post.
The game had been moved to Tuesday after the cold weather saw the original fixture
The win leaves Bournemouth just two points off the League One play-off places.
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Bournemouth boss Lee Bradbury told BBC Radio Solent:
"We knew patience was going to be key tonight and we've got to deal with that as teams are going to come here and play defensively.
"It was going to take time for the game to stretch out.
"Darryl pulled off a great save on the hour mark and that kept us in the game. Scott Malone also did fantastically well when he came on and was man of the match in the 20 minutes he played.
"It was great for Matt [Tubbs] to get his goal on his debut in front of the fans where he used to stand.
"There are a lot of teams looking for that fifth or sixth spot but if we keep playing the way we have then we will be in with a chance."