In a subdued opening, Carlisle showed they had no intention of providing an easy three points for the Albion.
Dobie, joining Stevens upfront, gave Kuipers a comfortable early catch with an effort from long range.
Kuipers carried on where he left off at Darlington with a confident catch from Galloway's free-kick from wide on the left.
Albion's first opportunity to put the visitors under pressure came via one of Mayo's long throw-ins, but Carlisle coped with the threat competently.
Watson and Dobie were lectured by referee Crick following an off-the-ball incident as Keen prepared to take a goal kick.
Carlisle achieved their first aim of keeping another sell-out crowd quiet as Albion struggled to find any attacking momentum.
Stevens, under pressure from Mayo, gave Kuipers another easy catch with a weak header in the 13th minute, by which time the Seagulls had yet to mount a worthwhile raid.
Adams generously retrieved the ball for Carlisle from the pitch when they were awarded a free-kick.
It was taken by Galloway and grabbed at the second attempt by Kuipers under stern pressure from Whitehead.
A square pass by Watson, intercepted by Connelly in the centre circle, enabled the visitors to break smartly. Stevens wasted the opportunity though with a poor cross.
Albion needed something to happen and Watson obliged in somewhat fortunate fashion in the 21st minute.
The fullback's inswinging cross from the right flank was dummied in the middle of the box by Zamora, which deceived Keen as the ball found its way into the far corner. 1-0.
Watson's third of the season, all at home, gave the Seagulls the incentive to stamp some authority on the contest and emphasise the yawning gap separating the sides in the table.
Hart just failed to get on the end of Mayo's deep cross, as Albion gradually began to take charge.
Gordon Connelly was cautioned on the half-hour for upending Mayo right in front of an incensed Carlisle dugout.
Minutes later Albion were saved by the woodwork.
Mick Galloway's inswinging corner was flicked on by Connelly for Inglis to rattle the top of the crossbar with a header.
It was a warning for the Seagulls, because they were still struggling to find any rhythm on a pudding of a pitch.
Albion had not really done enough so far to deserve their lead and Carlisle snatched a freakish equaliser three minutes before the break.
Kerry Mayo was trying to hook clear a Galloway corner to the near post when it sliced off his boot and over Kuipers into the far corner. 1-1.
It was indicative of an error-strewn half and gave battling Carlisle a real lift.
Rogers almost regained the lead for the Seagulls in first half stoppage time, but his effort was blocked by Keen after Zamora latched on to Cullip's through ball.
Just minutes after the restart, Bobby Zamora got up to put Albion back in front with his tenth of the season, all of them scored at Withdean.
Cullip escaped at the near post to head Watson's free-kick goalwards. It was blocked by Keen, leaving Zamora a simple task to nod in the rebound from point blank range. 2-1.
Jones then shot narrowly wide, but Watson gave Albion breathing space when they were awarded a penalty in mysterious circumstances on 61 minutes.
Referee Crick pointed straight to the spot from his corner, apparently for an offence by Prokas and Watson sent Keen the wrong way. 3-1.
Seconds later Stevens missed a glorious chance to reduce Carlisle's arrears, heading wide from Dobie's cross.
It was an expensive miss as Steele pounced to put the Seagulls 4-1 ahead on 65 minutes.
The ball broke to him after some untidy Carlisle defending and he slotted his second goal in as many games.
Team news: Lee Steele made his long-awaited full debut for Albion at Withdean today.
The summer signing from Shrewsbury replaced the suspended Charlie Oatway for the clash against crisis club Carlisle.
Steele came on to score the winner at Darlington last Saturday after replacing the injured Oatway.
Steele's place in the starting line-up meant a switch back to 4-4-2 from the 4-3-3 system employed so successfully by boss Micky Adams since early September.
Topscorer Bobby Zamora played alongside an orthodox strike partner, while Oatway's absence created a space on the bench for teenage frontman Scott Ramsay.
Also among the replacments for the 16th match in succession was Rod Thomas against one of his old clubs.
Carlisle manager Ian Atkins gave debuts to his two new midfielders, Mick Galloway and Gordon Connelly.
Albion: Michel Kuipers, Paul Watson, Kerry Mayo, Danny Cullip, Paul Rogers, Gary Hart, Richard Carpenter, Lee Steele, Nathan Jones, Matthew Wicks, Bobby Zamora. Subs: Crosby, Brooker, Thomas, Ramsay, Melton.
Carlisle United: Peter Keen, Mark Birch, Lee Maddison, Stuart Whitehead, John Inglis, Mick Galloway, Scott Dobie, Gordon Connelly, Ian Stevens, Mark Thurstan, Richard Prokas. Subs: Darby, Halliday, McAughtrie, Lee, Thwaites.
Referee: Mr D. Crick (Worcester Park, Surrey).
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