Despite battling back from two goals down to force overtime, the Giants could not get the extra point on the board as Cole Sanford won it in the extra period for the Welsh visitors, which sees Adam Keefe's side's lead cut to four points in the standings.
The Devils struck first just over a minute into the game as Justin Crandall threw the puck on goal and Sam Jardine was there to divert it into the net at 1:11 (0-1) and they doubled their lead at 6:31 when Joshua Waller went on the breakaway and finished high past Tyler Beskorowany (0-2).
The Giants got on the board only 26 seconds later when Donovan Neuls found Matt McLeod in the slot and the winger was able to finish through the pads of Ben Bowns (1-2) but Crandall produced another breakaway finish at 8:07 to restore the visitors' two-goal cushion (1-3).
The Giants managed to play out penalties on Scott Conway (hooking) and Ciaran Long (slashing) to end the period, although the Devils thought they had a fourth when Ryan Penny rifled home on the powerplay but it was ruled out for high-sticking, while a holding call on Jake Coughler went unpunished by the hosts.
Sanford was at the forefront of the Devils' early forays in the middle frame as he set up Joey Martin, only for Beskorowany to make a huge save, before his own breakaway effort went wide before the momentum swung back in the Giants' favour.
Cullen was called for a clipping penalty that got the SSE Arena crowd on its feet and when the Giants killed off that penalty, they made it a one-goal game at 32:34 when David Goodwin put the puck back in front for Steven Owre to finish from close range (2-3).
And when Cardiff ran into penalty trouble towards the end of the period as Trevor Cox took a charging call and Martin was penalised for slashing, Mark Cooper produced the equaliser at 39:16 as he jammed the puck in from close range through the pads of Bowns (3-3).
With the game in the balance, both sides saw chances hit the iron as Long struck the bar with a hopeful shot from the half-boards, while Cox beat Beskorowany on the breakaway but couldn't beat the frame of the goal as it ricocheted away.
Jake Coughler thought he had won it for the Devils when he put them ahead once more at 50:44, cutting inside and beating Beskorowany with a beautiful solo finish (3-4), but Scott Conway had other ideas as he found the rebound in the slot of McLeod driving the crease and scored the equaliser at 52:40 (4-4).
The same man nearly won it for the Giants in regulation with just over a minute to play, the puck coming across the face of goal for the Giants' leading scorer to snap a shot away but it hit the bar and stayed out.
Unfortunately the Giants were put on the back foot when Beskorowany was penalised for tripping midway through the period and that would lead to Cardiff's winner on the powerplay, Marcus Crawford feeding Sanford in the left circle and he made no mistake with the one-time finish for the game-winner and the extra point at 62:42 (4-5).
The Stena Line Belfast Giants are back on home ice at The SSE Arena, Belfast next Friday 24th March, as they face Sheffield Steelers in more ViaPlay Elite League action. Tickets are on sale HERE!