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.

The star slid off the circuit at Dunsfold Aerodrome in Surrey while recording his slot for the opening episode of the latest series.
On Twitter he said: "I'm driving for the first time ever today, on a race track, on tv. Wish me luck."
Kiefer Sutherland and Will Smith will also appear in the new series.
Sheeran managed to drive off the test track a few times and admitted he'd never driven a car ahead of the recording.
Johnny Vegas drove round the track in the now retired Suzuki Liana with big L plates on the top of the car in 2003, while Jack Whitehall didn't have a driving licence either and drove an automatic version of the Vauxhall Astra in series 21.
Top Gear's track was added to Google Street View last year.
The show's test driver, The Stig, was followed by a Google car round the 1.75 mile (2.82km) circuit so it could be mapped.
The latest series, the show's 22nd since its relaunch in 2002, is to start with a simultaneous broadcast in more than 50 countries.
The programme will be seen in Australia, Africa and the Middle East at the same time as it is shown on BBC Two.
A further 10 countries including Malaysia, Taiwan and Mongolia will screen it within 24 hours of its UK debut.
Ed Sheeran's Top Gear appearance is on Sunday on BBC Two at 20:00 GMT
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Bloemfontein joins Beijing and Lisbon in being suspended from carrying out any Wada-related anti-doping activities, while Moscow's lab had its accreditation revoked in April.
The decision leaves 31 Wada-accredited labs in the world, but none in Africa.
Wada said the laboratory may apply for reinstatement before 30 September.
The body did not disclose the reasons for the South Africa facility's suspension, which can be appealed against at the Court of Arbitration for Sport within 21 days of Bloemfontein being notified.
Belfast Giants remain within four points of Elite League leaders Cardiff Devils after earning a 5-1 Boxing Day away win over Braehead Clan.
[NEXT_CONCEPT]
Ed Sheeran, who doesn't have a driving licence, has managed to drive Top Gear's "reasonably priced car" off the show's race track.
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South Africa's Doping Control Laboratory has become the fourth lab to be sanctioned by the World Anti-Doping Agency (Wada) in the past month.