Brighton relied on containment tactics to keep a rampant home side at bay and as a result goalmouth action was kept to a minimum with neither goalkeeper seriously tested in a goalless first half.
The Black Cats twice appealed in vain for a penalty kick when both Lawrence and Carl Robinson were sent sprawling.
The determination of Jeff Whitley set up the chance for Marcus Stewart to test Michael Kuipers with a low drive and then Stephen Elliott lifted a left-foot shot over the bar.
The probing skills of Arca down the left flank caused endless problems with Kuipers cutting out a dangerous centre and a Robinson free-kick blocked just short of the line.
The Seagulls rarely threatened, Darren Currie chipping straight into the arms of Thomas Myhre who was again deputising for the injured Mart Poom.
But on the stroke of half-time the best chance of the half fell to Brighton. Sunderlands Norwegian international keeper had to fling himself to his right to hold on to a Charlie Oatway header from Leon Knight's centre.
Sunderland's pressure finally paid dividends in the 64th minute. Lawrence cut in to lash his shot against the bar, Kuipers denied substitute Michael Bridges from the follow up but was unable to prevent Arca from firing home the loose ball.
Bridges failed to hit the target when set up by Arca and when the pair combined to give Elliott the easiest of chances, the former Manchester City striker lifted his effort over the bar from close range.
Sunderland put the issue beyond doubt in the 81st minute when referee Phil Joslin finally answered home fans and players alike for a spot kick when Harding upended Lawrence in the box.
The former Mansfield winger gleefully slotted home the penalty and with the pressure off, Sunderland kept possession without threatening to run riot.
The 1200 Albion Fans were excellent throughout with a non-stop display that put the home fans to shame.