Due to drainage issues causing parts of the pitch to collapse, the Dons were forced to reschedule their home matches against Newcastle in the Carabao Cup, as well as league games against Accrington and Crewe.
The Wimbledon fans did not have to wait long to witness their side's first goal at home since mid-September as Stevens headed James Tilley's cross into the bottom left corner in the seventh minute.
Tilley went close from a free-kick shortly after, and he almost set up his side's second with a clever pass across Carlisle's six-yard box.
Visiting goalkeeper Harry Lewis saved Alistair Smith's long-range effort in the 39th minute, only to see Stevens convert the rebound to double Wimbledon's lead.
TrendingIt was 3-0 before the break when a corner sparked a melee in the box, leading to Cameron Harper turning the ball into his own net.
Stevens completed his hat-trick just after half-time, popping up at the far post to head in another excellent Tilley delivery.
The visitors finally put Johnnie Jackson's side under pressure during the final 20 minutes, but they could not find a consolation goal.