The Saints were well beaten at Sandy Park after a relentless display from the title chasing Chiefs.
Already missing the likes of Stephen Myler, George North and Louis Picamoles, the Saints lost skipper Tom Wood as a late injury withdrawal before kick off and Courtney Lawes shortly into a draining first half on the defensive in the South West.
While JJ Hanrahan's early score kept things close at the turnaround, the home side continued to dominate proceedings and chalked up six tries to coast clear in the second half, meaning the Saints' Champions Cup hopes will come down to a final day showdown with Harlequins at Franklin's Gardens next Saturday.
Straight from kick off the Chiefs went about their usual patterns, keeping the ball for dozens of phases and some five minutes to go from inside their own 22 up to the Saints'. But despite missing touch with a penalty clearance, the Saints' intensity without possession kept Exeter under the cosh and upfield a loose pass was snared by Hanrahan, who coasted behind the posts before converting.
While the visitors hd taken the lead, the theme of the game wouldn't change, Chiefs continuing to boss things in the middle of the park before two nearly moments for Jack Nowell and Stuart Townsend. Both knocked on with the line beckoning, Lion Nowell brilliantly denied by an instinctive hit from Ace Tuala but the Saints could only soak up the Exeter siege for so long.
When the Chiefs got bodies around Don Armand, the remarkable rearguard effort finally cracked and there was no stopping the powerful surge over the line that followed.
Steenson's conversion levelled things up and when the hosts returned moments later, they not only went ahead through Olly Woodburn's smart finish, but also found themselves a man up when Ken Pisi was shown yellow for a knock on deemed deliberate by the TMO and referee JP Doyle.
There was more pressure to come and while the Saints saw it out until half-time, there was no letting up from the home side. Woodburn breached the 22 less than a minute after the restart and Ian Whitten spotted a mismatch with David Ribbans, the centre gliding around the second row to dot down Exeter's third.
A brief bright spot followed for the Saints, but when a lineout inside the Chiefs 22 and a Hanrahan break came to nothing, Exeter returned with interest. Another lung-busting set on their own line ensued and while the outstanding David Ribbans denied Luke Cowan-Dickie, the bonus point was chalked up by Nowell after the umpteenth trip to the TMO of the afternoon.
Sam Hill burst through and stepped the cover to notch up try number five, Woodburn doubling up for a sixth after good work from Nowell and while Tuala powered into the corner with the final play, it was to be little consolation for the long journey home.
5mins SAINTS Try & Con Hanrahan 0-7
27mins CHIEFS Try Armand Con Steenson 7-7
32mins SAINTS Yellow K Pisi
33mins CHIEFS Try Woodburn 12-7
HALF-TIME CHIEFS 12-7 SAINTS
42mins EXETER Try Whitten 17-7
57mins EXETER Try Nowell 22-7
69mins EXETER Try Hill Con Steenson 29-7
78mins EXETER Try Woodburn Con Simmonds 36-7
80mins SAINTS Try Tuala
FULL-TIME EXETER 36-12 SAINTS
Turner; Nowell, Whitten, Devoto, Woodburn; Steenson, Townsend; Rimmer, Yeandle (capt), Holmes, Dennis, Parling, Ewers, Armand, Horstmann
Cowan-Dickie, Moon, Williams, Atkins, Salvi, Chudley, Simmonds, Hill
Tuala; K Pisi, Burrell, Mallinder, Foden; Hanrahan, Groom; A Waller, Hartley (capt), Brookes, Day, Ribbans, Lawes, Gibson, Harrison
Haywood, Ma’afu, Denman, Ratuniyarawa, Dickinson, Dickson, Tuitavake, Estelles