Taylor Vickerman, Trevor Cheek and Riley Kieser scored in regulation for Vancouver (6-13-0).
Brett Roulston and Jari Erricson scored within a span of 28 seconds with less than three minutes remaining in the game to force overtime and then a shootout for Prince George (7-10-3). Alex Forsberg had a first-period goal for the Cougars, while Zach Pochiro and Colin Jacobs scored in the shootout.
Goaltender Payton Lee was having a near-flawless game in net for the Giants until those forgettable dying seconds, recording 37 saves from 40 shots. He atoned for those late Cougar strikes with a strong showing in the shootout.
Mac Engel made 23 saves as Prince George slipped to their fourth straight loss.
Vancouver was able to make up for the absence of top goalscorer Marek Tvrdon — who suffered an undisclosed injury during the warm-up.
The Giants converted one of their four power-play chances while the Cougars were dismal, going 0-for-6.
Playing its third game in as many days, Prince George opening the scoring after just 36 seconds through a back-handed shot by Forsberg – his fifth of the season.
But with less than six minutes remaining in the first period, the Giants drew level when Vickerman was on hand to tuck in the short rebound after a shot by Mason Geertsen.
It was Vickerman's first goal and first point of the season.
Vancouver then took the lead at 18:12 during a 5-on-3 situation when Cheek received a centring pass from Anthony Ast and swept the puck home for his seventh goal of the season.
The Giants increased their lead 3:49 into the second period when Kieser sprinted towards the net and beat Engel with a cool left-handed finish.
It was a different story at the other end of the ice as Lee went on to savour a stellar second period, turning away all of Prince George's 15 shots — with the bulk of them coming in four power-play situations for the Cougars.
Going into the game, Vancouver had the worst penalty-killing record for a home team in the WHL, but the Cougars failed to capitalize and instead lived up to their billing as the second-worst power-play team in the WHL.