Berahino, on loan West Brom, struck either side of the break to make it four goals since his move from The Hawthorns.
He was on hand minutes before the interval to lash home a bobbling ball from close range after Jake Bidwell’s free-kick.
Exeter’s cause was not helped when skipper David Noble was shown a straight red card for an elbow on Bees defender Harlee Dean just after the hour mark.
The visitors’ misery was compounded a minute later when Berahino headed home Adam Forshaw’s right-wing cross unmarked at the far post.
City came closest in the first half when veteran striker Jamie Cureton got behind the home defence, but saw his effort blocked at close-range by goalkeeper Simon Moore, while Berahino might have grabbed his first ever hat-trick but for a save at the foot of his post by Grecians goalkeeper Artur Krysiak.