Phoebie Poole netted twice in the space of two minutes, opening the scoring with quarter of an hour to go, before substitute Adele Lindbaek grabbed the third goal in stoppage time.
The first half featured little goalmouth action, with the closest to an opener coming after 20 minutes when Poole pulled the ball back for Zoe Barratt, whose shot came back off the foot of the post.
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United sparked into life after the break, and nudged in front when Barratt drove down the right-hand side, cut infield and found Poole, who steered the ball home from inside the penalty box, guiding her shot past Sophie Giles.
Ninety seconds later, the U’s found themselves two goals in front. A corner from the right saw a deflected header smartly saved by Giles, but the rebound fell nicely for Poole, who scrambled the ball over the line.
United kept a level of control in the closing stages, and in the sixth minute of stoppage time, put the icing on the cake.
Lindbaek broke through the Exeter defence and rifled home her first goal for the U’s after joining the club at the end of August.
The victory took United up to fourth in the Southern Premier Division, level on points with all three sides above them.
League leaders Ipswich Town have a game in hand though, as do fifth-placed Watford, who are three points behind the top four sides.