The Belfast Giants lead the Elite League by seven points after they won in Edinburgh and nearest rivals Sheffield beat Braehead on Saturday.
Richard Hartman gave Edinburgh the lead but Adam Keefe equalised and in the second period Jeremy Rebek and Mike Hoffman put Belfast into a 3-1 lead.
Bari McKenzie got one back but Belfast scored quick goals through Graeme Walton, Jon Pelle and Robert Dowd.
Jan Safar got a third for the Capitals but the Giants claimed the vital win.
Doug Christiansen's men play Edinburgh again in the Elite League at the Murrayfield Ice Rink on Sunday at 1800 GMT.
Second-placed Sheffield Steelers have a home game against the Cardiff Devils.