Sireli Naqelevuki's second-half try proved enough for the Chiefs to send Saracens crashing to a 14-12 defeat, their first Premiership loss of the season, at a wet and windy Sandy Park on Sunday.
The 31-year-old, playing at centre, made the most of Chris Ashton's sin-binning for reckless charging moments before to score the winning try in the 54th minute.
Three penalties from Ignacio Mieres were also vital for the Chiefs as four from England flyhalf Owen Farrell ensured Saracens at least left with a bonus point.
Farrell had the chance to win it following Chris Whitehead's yellow card soon after Naqelevuki's try but he sent the resulting penalty wide as Saracens lost for the first time.
The Chiefs almost took the lead in the ninth minute when scrumhalf Haydn Thomas charged down opposite number Neil de Kock's kick from a line-out.
But Saracens were equal to charges from Carl Rimmer and James Phillips before hooker Whitehead knocked on with the line at his mercy.
It took until quarter-of-an-hour in for the deadlock to be broken and when it was there was nine points in six minutes with Farrell registering the first three.
The Saracens flyhalf kicked two simple penalties in front of the posts either side of a Mieres reply for the Chiefs with a far tougher chance.
Mieres missed a chance to draw the Chiefs level for a second time on 26 minutes by the slimmest of margins when he hit the post from a second penalty.
But a De Kock knock-on when the ball rebounded back in gave the Chiefs a good scrum position and some neat attacking play eventually saw Saracens captain Kelly Brown sent to the bin.
Mieres made no mistake with the second attempt and he then struck a mammoth penalty with six minutes left, just feet inside Saracens’ half, to put the Chiefs into a 9-6 lead.
Saracens were level five minutes into the second half when Farrell slotted a penalty after the Chiefs were penalised for hands on the ball following a scrum.
And just when Saracens thought they would be able to build some momentum, Ashton was sent to the bin for reckless charging.
It didn't prove costly immediately as Mieres missed the resulting penalty but it eventually did as Naqelevuki scored the first try of the game in the 54th minute.
The Chiefs exposed the space left by Ashton and following a line-out, Will Chudley fed Matt Jess who released to Naqelevuki to score, however, Mieres couldn't convert.
Farrell reduced the deficit to 14-12 with a penalty after the Chiefs were caught offside as the rain began to pour harder at Sandy Park.
And just as Ashton was ready to come on, the Chiefs were down to 14 as Whitehead was shown yellow for slowing the ball, however, Farrell missed the penalty that followed.
James Short came close with six minutes left only to be prevented by great covering defence from the Chiefs while in the last seconds, Steve Borthwick knocked on with Saracens close.
For the Chiefs:
Pens: Meres 3
Pens: Farrell 4
Exeter: 15 Luke Arscott, 14 Phil Dollman, 13 Ian Whitten, 12 Sireli Naqelevuki, 11 Matt Jess, 10 Ignacio Mieres, 9 Haydn Thomas, 8 Richard Baxter, 7 James Scaysbrook, 6 James Phillips, 5 James Hanks, 4 Tom Hayes (captain), 3 Carl Rimmer, 2 Chris Whitehead, 1 Brett Sturgess.
Replacements: 16 Simon Alcott, 17 Ben Moon, 18 Chris Budgen, 19 Aly Muldowney, 20 Ben White, 21 Will Chudley, 22 Gareth Steenson, 23 Jack Nowell.
Saracens: 15 Alex Goode, 14 Chris Ashton, 13 Duncan Taylor, 12 Brad Barritt, 11 James Short, 10 Owen Farrell, 9 Neil de Kock, 8 Jackson Wray, 7 Will Fraser, 6 Kelly Brown (captain), 5 Mouritz Botha, 4 Alistair Hargreaves, 3 Carlos Nieto, 2 Jamie George, 1 Mako Vunipola.
Replacements: 16 Schalk Brits, 17 Rhys Gill, 18 Matt Stevens, 19 Steve Borthwick, 20 Ernst Joubert, 21 Richard Wigglesworth, 22 Charlie Hodgson, 23 Joel Tomkins.