Exeter ended a run of six games without a win in all competitions as they went top of Pool One of the LV=Cup and denied Northampton progress to the knockout stages of the competition.
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The Chiefs will have to wait for the result of Sunday's game at the Brewery Field to see if they are pipped to a semi-final place by Harlequins, who only need a point from their game against Ospreys.
Exeter dominated the scoring in the first half and led 22-5 at the break after tries from Ben White, Jack Nowell and a first touchdown from Watisoni Votu, with Ignacio Mieres adding two conversions and a penalty to an Alex Waller try.
Northampton looked a refreshed side at the start of the second half and they reduced the arrears with two tries from Lee Dickson, both converted by Stephen Myler, with Mieres replying with two penalties.
Openside flanker Ben White opened the scoring for the Chiefs after eight minutes from close range after right wing Watisoni Votu ran through a number of tackles down the right touchline.
They increased their lead as centres Ian Whitten and Josh Tatupu linked up to split the Saints defence as they spread across the pitch and, with a man overlap, full-back Nowell went over in the left corner.
A third try soon followed with lock Damian Welch stopped short of the line, but the ball was recycled for Votu to cross.
Mieres added the conversion and just after the half hour he increased the home side's lead with the first penalty of the game.
Northampton kicked a couple of penalties to touch and from the second they drove over the Exeter line with loosehead prop Waller getting the touchdown, but it was the Chiefs who led 22-5 at half-time.
The visitors looked a different side at the start of the second period but the Exeter defence stood firm and the Saints brought on the cavalry as they introduced five replacements, three of them in the pack.
Saints tried to mount another attack through skipper Ben Foden but the pass from the England international to wing James Elliott was well read by Votu to extinguish the move.
The visitors kicked two more penalties to touch as they searched for a try, and at the next infringement White was sent to the sin-bin. From the catch and drive it was replacement scrum-half Lee Dickson who got the touchdown.
Replacement fly-half Myler added the conversion to reduce the arrears to 10 points, but that was shortlived as the Chiefs were quickly back into the Saints 22 and Mieres slotted two penalties between the uprights.
The Saints went in search of more tries with Foden going over in the corner, but the try was ruled out for a forward pass. Exeter were then reduced to 14 men when replacement lock Will Carrick-Smith was yellow carded.
Northampton used their man advantage as they pushed the Chiefs back over their own line and Dickson picked up at the back to dive over the line. Myler's conversion reduced the arrears to nine points with five minutes remaining but that was the end of the scoring.