Five points were greatly needed by the Chiefs too and it was they who comprehensively stole a march with three tries inside the opening 27 minutes. Alex Waller shortly before the break and Lee Dickson, twice, after gave the Saints a glimpse of a remarkable fightback but the damage had already been done and their hopes of silverware now hang soleley on the Aviva Premiership.
Having perhaps shaded the early exchanges, Watisoni Votu's barnstorming 40-metre counter charge compounded that claim and when the forwards took over the impetus, Ben White's route to the line was a straightforward one with defenders committed beneath the posts.
They were in again on 15, too, Josh Tatupu on Ian Whitten's shoulder in midfield to cut through and with the ball moved wide, Jack Nowell was in the corner with a man to spare outside.
Having maximised the first score, Ignacio Mieres hooked the conversion wide, but with Saints frustrated in their immediate attempts to hit back, the Chiefs made it three - Votu burrowing over after possession had switched hands with an early hit at the scrum.
A piercing break from Luther Burrell catapulted Saints forward but after a penalty was conceded for holding on, in a matter of minutes Mieres was extending the home lead to 22 points from the tee, Saints again falling foul at the breakdown.
A monumental task was already facing the visitors but they would get a small foothold before the break, Alex Waller driven over for a second try in as many games as a patient maul crabbed back and sideways before motoring over the Exeter line.
Having survived unscathed from Exeter's spell of territory at the start of the second 40, the Saints would produce the game's next score too, again through their dominance in the forwards. The field possession for a series of five-metre line outs was earned by a crisp attack spearheaded by Ben Foden and with Chiefs try scorer White sent to the bin for a third penalty offence in quick succession, Dickson touched down an ominous score.
His half-back partner Stephen Myler converted but the good work was almost immediately undone, Mieres dinking over an easy penalty under the posts to take the lead back to three scores - a margin consolidated by the Argentine's third success some four minutes later.
In any case, Saints still needed to score two more tries as well as turning around the 16-point deficit. A forward pass denied James Wilson one of those scores after a fine finish but with Saints awarded a penalty from the resulting scrum, not to mention a yellow card for Will Carrick-Smith, their slim hopes remained alive.
With the pack again flexing their muscles, this time at the scrum, a penalty try looked almost certain but Dickson instead benefitted again from the power for his second of the evening to reduce the requirements to two scores, but the Chiefs' infringements had wound the clock down to just four minutes.
A Ben Nutley surge and some superb offloading from Samu Manoa and Soane Tonga'uiha thrust them onto the front foot once again but it was Exeter who ended the game close to the Saints line and with a victory their opening burst had deserved.
8mins CHIEFS Try White Con Mieres 7-0
17mins CHIEFS Try Nowell 12-0
27mins CHIEFS Try Votu Con Mieres 19-0
32mins CHIEFS Pen Mieres 22-0
35mins SAINTS Try A Waller 22-5
HALF-TIME CHIEFS 22 SAINTS 5
59mins CHIEFS Yellow White
60mins SAINTS Try Dickson Con Myler 22-12
64mins CHIEFS Pen Mieres 25-12
68mins CHIEFS Pen MIeres 28-12
73mins CHIEFS Yellow Carrick-Smith
75mins SAINTS Try Dickson Con Myler 28-19
FULL-TIME CHIEFS 28 SAINTS 19