The match was poised at 17-14 at half-time but Saracens powered home to win the try count seven to four.
Saracens director of rugby Alex Austerberry said: "Credit to Exeter, they never go away and they were always in the fight throughout.
"For us, we started well but we lost shape and momentum a bit which allowed them back into the game.
"In the second half I thought we were clinical and we managed to turn that momentum and pressure into points, which ultimately sealed the win."
In freezing conditions pressed and probed but Saracens struck first with a stroke of luck from the bouncing ball. Jess Breach collected her kick-through, with Poppy Cleall then setting Ella Wyrwas free for the opening score.
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