Despite atrocious conditions at St James Park, the first half was an entertaining affair. Alan Gow hit the crossbar for Exeter with a stunning effort from 25 yards and Jamie Cureton was denied by a smart Andy Warrington save low to his right.
At the other end, Exeter goalkeeper Artur Krysiak made two excellent saves from Alex Revell and Johnny Mullins before the deadlock was broken three minutes before half-time when Sharps glanced a near-post header across goal and into the net from a corner.
Exeter had plenty of possession after the break, but they did not test Warrington enough.
The Millers were reduced to 10 men three minutes from full-time when Mitchell Rose was given a straight red card for a foul on substitute Aaron Dawson.
Matt Oakley’s long-range effort was the closet the Grecians came to an equaliser, but Warrington showed a safe pair of hands to earn all three points for his side, who defended superbly throughout the second half.