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.

"The truth is that Taylor Swift and I are together, and we're very happy," the actor told the Hollywood Reporter.
"That's the truth," he continued. "It's not a publicity stunt."
Hiddleston has been speaking about his first Emmy nomination for The Night Manager, saying it was "fantastic" to to be up for outstanding lead actor.
Hiddleston played concierge-turned-spy Jonathan Pine in the BBC's adaptation of John le Carre's novel.
He was nominated on Thursday for the prize for lead actor in a miniseries or movie, alongside fellow Brits Benedict Cumberbatch and Idris Elba, and US stars Bryan Cranston, Cuba Gooding Jr and Courtney B Vance.
But it is speculation about his relationship with Swift that has been rife in the press since they were snapped embracing near Swift's home in Rhode Island last month. The images went viral online.
Hiddleston, 35, who is in Australia shooting reprising his Loki role in the latest Thor film, had previously refused to discuss the relationship with the press. There had been reports that they could have been filming a music video together.
"I'd rather just talk about my work if that's all right," he told one reporter in Queensland earlier this week.
But when asked by the Hollywood Reporter how he would "respond to people who claim that you're involved in some sort of publicity stunt", the British actor rejected the "notion".
The magazine reported that he laughed at the question and thanked them for asking it.
Swift was previously in a relationship with Scottish DJ Calvin Harris, who 'unfollowed' her on Twitter after images of the singer kissing Hiddleston appeared online.
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The employees, who worked in four takeaways, are alleged to have been living and working in the country illegally.
The firms have been asked to produce documents proving their staff had the right to work and live in the UK.
If they are unable to do so the Home Office said they would impose a fine of up to Â£20,000 per illegal employee.
The process to deport the workers is already under way.

Scott Flynn flagged down a police car and told officers "I want the jail" after stealing a bottle of juice and smashing a window.
Flynn was spotted putting two packages in his mouth at police headquarters in Dundee.
He planned on taking the drugs into Perth Prison to pay off a debt.
The 31-year-old claimed a gang said that he and family members would be "slashed" if he did not cooperate.
Depute fiscal Eilidh Robertson told Dundee Sheriff Court that the packages contained almost 40g of heroin and just over 3g of cannabis resin.
She said forensic officers had estimated the total maximum value of the heroin at £3,860.
"However, if the accused had intended to resell these drugs once remanded to prison then the value could be as much as five times that," she said.
Flynn admitted charges of theft, vandalism and being concerned in the supply of drugs on 8 November last year.
Defence solicitor George Donnelly said: "Sometimes those who are in debt are told they have to work off that debt.
"His work was to try to get these drugs in to Perth Prison.
"He was advised graphically that if he didn't he and member of his family would be slashed.
"They mentioned his sister and her baby, and his grandad who has dementia and cancer."
Sheriff Alastair Carmichael told Flynn: "You committed two offences with the intent of being arrested and taken in to the prison sector in possession of heroin.
"This is a serious matter."
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.
[NEXT_CONCEPT]
Tom Hiddleston has denied his romance with singer Taylor Swift is just for the cameras in his first comments on their widely reported relationship.
[NEXT_CONCEPT]
Eleven people have been arrested in Shetland following illegal immigrant raids by the Home Office.
[NEXT_CONCEPT]
A man who deliberately got arrested in an attempt to smuggle up to £20,000 worth of heroin into prison has been jailed for three years.