Colin Shields put Belfast ahead before Scott Aarssen levelled late in the first period.
However, second-period goals from Ryan Martinelli and Mark Garside left the Giants in control.
Alex Foster increased Belfast's lead to 4-1 before Steve Saviano completed the scoring with five minutes left.
Belfast have a game in hand on the Devils, who defeated Coventry Blaze 5-3 on Monday evening.
Cardiff are back in action against Blaze on Tuesday while the Giants are at home to Manchester Storm on Wednesday evening as the busy festive period continues.
The Giants took the lead after 15:52 on Monday with Shields netting after being set up by James Desmarais and Saviano.
Aarssen netted on the powerplay in the last minute of the first period but Martinelli restored the Giants' advantage on 27:41 after combining well with Saviano.
Garside then fired into the Braehead net on 33:50 before Foster's powerplay effort on 51:45 and Saviano's concluding goal on 55:18.
After Wednesday's game against Manchester, Braehead Clan are the visitors on Friday before Coventry Blaze take on the Giants at the SSE Arena on 2 January.
Belfast Giants remain within four points of Elite League leaders Cardiff Devils after earning a 5-1 Boxing Day away win over Braehead Clan.