Bournemouth were good value for their second away win of the season after a fine performance at Exeter.
Exeter started brightly and deserved to take the lead in the sixth minute. Andy Roscoe only had one thing in mind when he struck a powerful free-kick from the edge of the box and it flew through a crowd of players and into the bottom corner.
It looked like it would be a comfortable afternoon for the Grecians, but instead of pressing forward they sat back and allowed Bournemouth back into the game.
Carl Fletcher came close to equalising for the visitors when he thumped a powerful shot just over the bar from 25 yards.
Kevin Miller kept out a Derek Holmes header with his feet and Shaun Maher headed wide from Danny Thomas' corner.
Bournemouth deserved to pull level in the 35th minute. Alan Connell exchanged passes with Wade Elliott on the edge of the box before superbly lobbing the ball over Miller.
As the visitors continued to pour forward Alex Watson was harshly adjudged to have handled inside the box. Elliott stepped up and made no mistake from the spot.
After the break it was the visitors who continued to look the more dangerous. Stephen Purches forced Miller into action with a low shot from 15 yards.
Don Goodman headed just over for Exeter as the home side chased the game.
Santos Gaia was sent off midway through the half for his second bookable offence and from the resulting free-kick Gareth O'Connor lashed the ball into the back of the net from the edge of the box to put the result beyond any doubt.
Only a fine save from Miller prevented James Hayter from increasing the scoring in the final minutes.
Bournemouth boss Sean O'Driscoll commented: "Their commitment, their endeavour, their honesty and their hard work has been first class.
"It has been first class for a while and they got their rewards for that today."