The hosts were almost ahead inside the first minute when Danny Graham's scuffed shot was hacked off the line by Adam El-Abd. And half-an-hour later Bridge-Wilkinson gave Carlisle a lead they thoroughly deserved after full-back David Raven's 30-yard strike had been palmed away by Michels Kuipers.
Graham Kavanagh was on hand to cut the rebound back, allowing Bridge-Wilkinson to side-foot home from six yards out for Carlisle's first league goal in over 400 minutes. Brighton striker Stuart Fleetwood should have equalised after a smart interchange between ex-Carlisle duo Glenn Murray and Joe Anyinsah but the visitors never looked likely to stop the rampant hosts.
Simon Hackney and Graham both could have added further goals for Carlisle before winger Cleveland Taylor grabbed a second on the stroke of half-time. Some more sustained pressure eventually paid off for the Cumbrians when Taylor steered in a close-range volley from Graham's clever cross.
Ten minutes into the second half Bridge-Wilkinson dropped a shoulder 30 yards out and played a pass to Graham who returned the favour and the barrel-chested midfielder smashed a first-time drive into the roof of the net from 12 yards.
By that point the home side might already have been further ahead and out of sight had the tricky Hackney, Graham and Kavanagh done better in front of goal. With 25 minutes left, substitute Tom Fraser's short free-kick was smashed in by Matt Richards, courtesy of a deflection off Richard Keogh.
With the home crowd sensing another heartbreaking afternoon the Carlisle players stepped up a gear and the tide was too much in United's favour to let their seaside visitors back into the game. Hackney, with the clock deep into injury time failing to take a chance on the break to make the scoreline more emphatic for the Cumbrians.