The hosts broke the deadlock 13 minutes into the second period courtesy of a Colin Shields strike.
Steve Saviano doubled the lead midway through the third period before Shields sealed victory with 46 seconds left.
Belfast, who have played one game less than Cardiff, take on the Capitals again on Friday at the same venue.
Belfast Giants have closed the gap on Elite League leaders Cardiff Devils to six points with this comfortable win over the Capitals at the SSE Arena.