The powerful striker, on loan from Bolton, enjoyed an Easter Monday to remember with a display of quality finishing to badly dent Crawley's hopes of a late play-off charge.
Eaves broke the deadlock with an unstoppable drive from 25 yards three minutes into the second half.
He then ran from the halfway line before coolly lifting the ball over goalkeeper Paul Jones in the 64th minute.
Shrewsbury could even afford the luxury of a missed penalty, skipper Matt Richards blazing over after Yado Mambo's shirt was tugged by Joe Walsh, before Eaves completed his hat-trick five minutes from time with another blistering 20 yard thunderbolt.
Crawley had made much of the early running and Jamie Proctor, who had a loan spell with Shrewsbury earlier this season, looped a header just over after being picked out by Mustapha Dumbuya's cross.
Chances were few and far between for Shrewsbury in the first half with little to concern Jones, although he had to be alert to help a 20-yard curler from Steve McGinn round a post.
But that all changed after the restart as Eaves fired Shrewsbury to only their second win in nine home games.
Goalkeeper Chris Weale chalked up a clean sheet with fine stops from Mark Connolly's header and a Nicky Adams shot.