The Giants ended the Capitals four game winning home run and skated back to the top of the Elite league standings following a tight game in Scotland.
The visitors were never behind in this game and although it took until the second period for Capitals resistance to be broken, the Giants always looked the more likely and strikes by Brandon Benedict and Evan Cheverie, gave them a 2-0 lead to protect going into the third period.
Capitals gave themselves a glimmer thanks to a goal by Mark Smith with less than four minutes left but an empty net strike by Pat Batemen saw Giants overtake Coventry and take pole position in the standings.
Capitals had given as good as they got in the opening goalless session but fell behind at 25.14 when Benedict (14th) fired home. Giants then doubled their lead at 32.45 thanks to a finish from Cheverie (11th) and in a period where they outshot the home side by 16 to 5 they were in command.
The win boosts the Giants' title challenge as rivals Coventry Blaze lost 6-4 to Sheffield Steelers.
The victory completed a good weekend for Belfast as they had defeated Newcastle Vipers 11-3 on Friday night.
Steve Thornton's side next face Cardiff in the Challenge Cup semi-final first leg away from home on Wednesday and then play host to Coventry in a crucial league fixture at the Odyssey Arena next Saturday evening.
Period Scores: 0-0, 0-2, 1-1
Penalty Mins: Edi 4 - Bel 20
Powerplay: Edi 0/5 - Bel 0/2
Shots On: Cody Rudkowsky 34 + 1 ENG - Stephen Murphy 26
Referee: Moray Hanson
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