Adam Stansfield put the Grecians ahead with his ninth goal of the season in the 13th minute. Danny Hollands equalised after the break before Brett Pitman put the Cherries ahead and scored again in the final minutes to put the result beyond doubt.
Exeter started brightly and Dean Moxey had two early chances to put his side ahead so it came as no surprise when they took the lead.
Stansfield pounced on a loose ball and sprinted into the box before poking the ball past the advancing Jalal.
Bournemouth's best early chance came when Ryan Garry tried his luck with a long range shot which flew over the bar.
Bournemouth pushed forward as the half wore on but never looked like having the firepower to trouble well-organised Exeter.
On the stroke of half time Moxey picked out Steve Basham with a perfect cross and the striker's shot was well saved by Jalal as the Grecians attempted to stretch the lead.
After the break Alex Russell went close with a shot which was deflected narrowly wide.
Bournemouth almost equalised when Pitman let fly from 35 yards and struck the ball against the bar. Hollands then went close with a strike from 12 yards as the Cherries hunted an equaliser.
Bournemouth went ahead with two goals in five minutes. They were gifted an equaliser when City goalkeeper Paul Jones made a mess of his clearance and Hollands tapped the ball home.
Pitman then went on a fine run and blasted the ball past Jones from 15 yards. With two minutes left Jeff Goulding found Pitman who tapped home from close range to secure the win.