The two teams were fairly well matched thereafter and two Ryan Mills got Gloucester back within striking range at 10-6 but further scores from Foster and Walker-Blair settled the contest.
On the night, the Chiefs were well worthy of the win with Poluleuligaga and Sestaret the stand out performers.
Gloucester started well courtesy of a strong scrummage and Dan Robson and Gareth Evans tested the fringe defence only for a knock on to end the threat.
But it was the Chiefs who struck first courtesy of a powerful midfield break from Sestaret before two neat offloads, the latter from centre Sam Mills slightly forward looking, saw the supporting Poluleuligaga coast over. Myles Dorrian converted for 7-0.
A powerful break from Ryan Mills backed up by a good forward drive saw Gloucester hint at striking back but the Exeter defence held firm and relieved the pressure after earning a penalty for holding on.
There was plenty of endeavour in the next 15 minutes but neither team really looked like breaking through with both defences just doing enough to maintain the stalemate.
And it wasn't until the half hour mark that the scoreboard was troubled again as Dorrian slotted a straightforward penalty after a sharp blindside break from Poluleuligaga to open up a 10-0 lead.
Gloucester finally broke the defensive line as half time approached when Reuben Haile took a great angle off a short Mark Woodrow pass but was hauled down just short of the line to frustrate the home support.
Gareth Evans was then denied a try as he took a quick tap from the wrong place so Gloucester opted for a penalty from Ryan Mills who opened the home account to make the half time score 10-3 to Exeter.
Mills then had an early second half chance from the kicking tee as Poluleuligaga led with his forearm into a would be tackler and duly bisected the posts from near halfway.
The joy was short lived though as a midfield break saw Chad Slade throw a speculative pass towards the right wing and Mark Foster took the ball on the bounce at pace to sprint home from the 22. Dorrian curled over a lovely conversion from the touchline to make it 17-6 to the Chiefs.
The visitors were now looking full of confidence and another flowing move almost breach the Gloucester line. A penalty was conceded in the shadow of the posts and Dorrian had an easy kick for a 20-6 lead.
That lead was extended on 63 minutes when flanker Charlie Walker-Blair took advantage of a gaping blindside and romped home for the third score. Dorrian again converted.
Understandably given the scoreline, Exeter looked the sharper in the final stages but couldn't breach the Gloucester defence again in order to clinch the try scoring bonus point.
The referee blew for time early with Exeter's Blanchet down receiving lengthy treatment but, thankfully, he walked off the pitch unaided.