Two Owen Farrell penalties gave Sarries an early lead but Luke Cowan-Dickie's try and a Gareth Steenson penalty saw the home side go into the break ahead.
A Farrell penalty hit the post at the start of an error-strewn second half.
But scores from Harry Williams and Matt Kvesic, plus a penalty try, sealed the victory, with Ben Spencer's effort a mere consolation for Saracens.
The win moves Exeter three points above Saracens at the top of the table as they approach the midway point of the season.