The two late tries neatly bookended two early scores for Gloucester who started and finished well but who were made to work incredibly hard in the meantime.
The Chiefs had their moments with Josh Matavesi showing some silky skills and new signing Sireli Naqelevuki was a muscular presence on the wing while the pack completed gamely.
However, Gloucester had a little bit too much experience with the likes of Peter Buxton and Will James leading the way while some of the young talent on display in the backline scored the tries when it mattered.
Conditions were far removed from those experienced two days earlier with the pitch damp underfoot and a mist rolling in.
The early stages saw the referee struggling to get a solid scrummage platform with the Gloucester pack looking in good nick.
Exeter held out one strong forward push but couldn't regroup after a sharp break from Jordi Pasqualin and, after several phases of recycling, Tom Voyce forced his way over for a 5-0 lead after 21 minutes.
It was a good start from the home side and a second try duly followed when Jonny May ran onto a well weighted grubber kick to score untouched in the left hand corner.
Ryan Davis duly replied with two penalties as Exeter finally got some possession with Gloucester falling foul of the referee at the breakdown on several occasions.
It had been a strong riposte from Exeter and, with half time approaching, Sireli Naqelevuki almost made the line after an overthrown lineout in the Gloucester 22 bounced kindly for the visitors.
So, Gloucester went into half time with a 10-6 lead although the Chiefs could reflect upon a strong second quarter and with the momentum behind them.
Both sides made some obviously preplanned changes at the interval with Gloucester withdrawing Pasqualin and Narraway and the second half started in an untidy flurry of errors.
In fact the game reached the hour mark with no addition to the score and an ever increasing penalty and handling error count on both sides.
The deadlock was finally broken on 62 minutes when Henry Trinder stroked home a penalty from distance after replacement Matt Betty forced an infringement with an enthusiastic kick and chase.
However, a further try remained elusive with Matt Cox coming closest when tackled into touch near the Exeter line after a neat chip and catch from Jack Hayes opened up some space while Trinder lost the ball in contact as he drove for the line.
However, the pressure was building and an opening was eventually carved out for the lively Betty who skipped down the right hand touchline to dive over for Gloucester's third try which was excellently converted by Trinder for a 20-6 lead.
And, when Dan Robson sniped over from close range for the fourth try just two minutes later, the bonus point and the game were in the bag following another fine Trinder conversion.