Slater Doggett had put the Giants ahead in the first period, but Stephen Dixon tied it up on the powerplay at the end of the second and Brodie Reid then got the game-winner in the shootout for the visitors after Carruth's heroics.
It is only the Giants' second home defeat of the season and, despite taking one point from the game for losing in the shootout, they fall four points behind Premier Sports Elite League leaders, the Sheffield Steelers, and two points behind the second-placed Devils, who have played three games more.
The Giants were quicker out of the blocks and Jordan Boucher nearly gave them the lead early when Jeff Baum fired the puck across the face of goal but the winger couldn't get enough of a redirect on it to put it in.
But it would be the Giants who would strike first through Doggett, the centreman taking the pass from Ben Lake and skating into the slot where he ripped it past Devils goaltender Carruth to open the scoring at 3:23. (1-0)
Tyler Beskorowany - who was also excellent with 26 saves - was required to make a slick save to deny Cole Sanford, who one-timed Jake Coughler's reverse pass into the slot, and the Giants got to the intermission ahead when they killed off half of an interference penalty on Mark Cooper.
After playing out the remainder of Cooper's penalty, David Goodwin almost doubled the Giants' lead when Cam Knight threw the puck back out in front for the captain, but Carruth produced a superb point-blank stop to deny him.
The Giants' penalty kill produced the goods again when Lewis Hook went off for tripping and Goodwin had another big chance to add a second when he went on a two-on-one with Cooper and decided to shoot himself but only found the pad of Carruth.
Unfortunately it would not be third time lucky on the penalty kill for the home side as a too many men call proved to be their undoing, Dixon working his way free at the doorstep and jamming it under the pads of Beskorowany to tie it up at 39:32. (1-1)
A cagey third period saw both netminders keep the scoreline down as neither side risked over-committing and giving away a quality scoring chance, although the Giants looked the likelier to break the tie as they put a bit more pressure on Carruth.
They did need to kill off a high sticking call on Doggett, which they did comfortably, and they needed Beskorowany to make another big stop to deny Justin Crandall after he went in unopposed after a misplay at the blue-line from a Giants defenceman to keep it all-square.
And after Carruth did likewise at the other end to deny a late flurry of chances for Belfast, the final buzzer sounded, ensuring both teams would go away with at least a point for their efforts.
The Giants were handed a big chance to get the win in overtime when they went on the powerplay for the first time, Mark Richardson called for slashing, but the visitors shut the door as Carruth produced one impressive stop to deny Lake and take it into a shootout.
Lake was the first to find the net with the Giants' third effort in the shootout, with Sanford tying it up for the Devils on their fourth. Doggett then put the hosts back in front with their final shot but Sam Duggan, needing to score, beat Beskorowany to take it to sudden death.
With their first shot in sudden death, Reid got the winner for the Devils when he ripped it high past Beskorowany, earning the extra point for the visitors when Doggett couldn't reply as Carruth made his biggest save of the night. (1-2)
The Stena Line Belfast Giants are on the road for their next four games, starting with a trip to the Coventry Blaze on Wednesday February 9. The Giants return to home ice on Saturday 19 February when they welcome the Fife Flyers to The SSE Arena, Belfast. Tickets are available HERE.