Ken Pisi, Soane Tonga'uiha and GJ van Velze produced the tries in Devon which were supplemented by 15 points from the boot of the impressive Stephen Myler and some staunch defensive work interspersed throughout the 80 minutes.
Territory and possession may have been weighted marginally in the hosts' favour, but Saints showed that it's what you do when you have the ball that matters and denied their hosts even a losing bonus in their first home league defeat of 2012/13.
It took until the 13th minute for the scoreboard to start moving, Gareth Steenson kicking a penalty as Saints tacklers failed to roll away, but it was the visitors who would make the first telling break of a congested game.
Ben Foden flew through Luke Arscott's attempted tackle having fielded a poor kick from the Chiefs full back and Ken was the beneficiary of the scything burst, coasting beside the posts despite Matt Jess' presence.
Extras added, Foden almost laid on a second try just four minutes later, popping up on the opposite wing and passing marginally forward and beyond Jamie Elliott's reach.
Still, the Saints stayed in control, both in defence and at the set piece and while one brutal shove from Paul Doran Jones went unrewarded, when Hoani Tui buckled at the very next scrum Myler rewarded his tighthead's power.
It was Doran Jones' cover tackle that halted a dangerous break from Chiefs hooker Neil Clark too, while Ian Whitten showed similar nouse in defence to field Myler's teasing kick through close to his own line.
It wasn't long before the Saints were making their pressure count, Doran Jones again finding a superb angle and drive on Tui once more. Having thumped an upright with a gimme just moments earlier, Myler refund his form and slotted the three points from wide on the left to open up a 10-point gap.
Having had little joy from the opening period though, Exeter continued to probe and referee Greg Garner produced the harshest of yellow cards when Dylan Hartley conceded the Saints first penalty for some 25 minutes.
Not that the hosts weren't complaining and with Steenson compounding the call with a second penalty there was just a score between the sides at the break.
With the Saints a man light for another eight minutes though, Exeter quickly made the most of their numerical advantage in the scrum but Steenson's penalty was swiftly cancelled out by a 40 metre effort from Myler.
The gap would be four though when Hartley returned, Chiefs again putting the pressure on and winning the sin bin period 9-3 thanks to another Steenson kick.
Yet when another dangerous Chiefs foray ended in turnover ball, Myler's kick and chase along with Ken forced the home side into touch 15 metres out. The first wave of Saints attack was illegally halted, but with advantage in the bag, Myler went to the corner and Tonga'uiha was ominously driven over.
The game continued to follow it's pattern and when it was Exeter's turn to attack they finally found the cutting edge to breakdown the Saints, Sireli Naqelevuki powering over from close range after a bruising spell of defence for the visitors.
With Ignacio Mieres adding the conversion an engaging tie was again back to within a score and a brilliant turnover from Dom Waldouck allowed Myler to pump his side back into Chiefs territory. Having survived an interception scare the men in blue played the patience game and a second Myler kick to the corner was first set and then slowly pushed over in the hands of van Velze.
A fine conversion from dead-eye Myler crucially took the Saints two tries clear and while there were attempts from both sides to secure an extra point, the final whistle brought a welcome end and substantial easing of the hurt from MK.
The biggest focus now will be carrying that momentum into a huge upcoming period that will make or break their 2013.
13mins CHIEFS Pen Steenson 3-0
19mins SAINTS Try Ken Con Myler 3-7
27mins SAINTS Pen Myler 3-10
34mins SAINTS Miss pen Myler
36mins SAINTS Pen Myler 3-13
38mins SAINTS Yellow Hartley
39mins CHIEFS Pen Steenson 6-13
HALF-TIME CHIEFS 6 SAINTS 13
43mins CHIEFS Pen Steenson 9-13
45mins SAINTS Pen Myler 9-16
47mins CHIEFS Pen Steenson 12-16
59mins SAINTS Try Tonga'uiha Con Myler 12-23
66mins CHIEFS Try Naqelevuki Con Mieres 19-23
75mins SAINTS Try van Velze Con Myler 19-30
FULL-TIME CHIEFS 19 SAINTS 30