Alberta now has 15 championship banners in the program's storied history.
"To be honest, this is probably the ugliest win of the year, but good teams find a way to win," said Alberta captain Kruise Reddick.
The Golden Bears jumped ahead early when Colin Archer made a great rush to gain the offensive zone and set up Stephan Legault with a nifty cross-ice pass. Legault wristed a shot high on the short side of UNB goalie David Shantz.
Alberta made it 2-0 on the power-play when Jordan Hickmott, the Golden Bears' top sniper in the regular season, beat Shantz with a screened shot.
The Varsity Reds showed some spark early in the second and cut the lead in half when Dylan Willick caught Alberta goalie Kurtis Mucha off guard after Matt Boudens made a slick backhand pass from behind the net.
UNB almost tied it midway through the second period when Taylor MacDougall blasted a slapshot off the post.
The Varsity Reds had another great opportunity to tie it when they had back-to-back power plays, but didn't get any decent scoring chances. The double penalty kill was a pivotal moment in the game.
"It was huge," Reddick said. "The guys all stuck together, they were blocking shots and getting pucks deep."
Alberta's Johnny Lazo redirected a nice no-look pass from Levko Koper to make it 3-1 with just 3.6 seconds left in the second period.
Phillippe Maillet deflected a point shot from Dana Fraser 7:55 into the third period to cut the lead back down to one goal.
Reddick scored the clincher when he put a wrist shot through a crowd with UNB trying to kill a too-many-men penalty. That made it 4-2 Alberta.
Adrian Robertson brought UNB to within one goal again with a point shot that flipped high over Mucha before dropping into the net.
With UNB pressing for the equalizer, Koper finished off a rare 2-0 rush to pot a short-handed goal at 17:24 and make it 5-3. Jordan Rowley added another short-handed marker into an empty net with 1:49 left.
This was the third time the teams met in the CIS final. Alberta won in double overtime in 2000 and edged UNB 3-2 in 2008.
Cam Braes, like all his teammates, felt disappointment with his silver medal.
"In the moment it feels like you got stabbed in the heart," said Braes, a third-year forward. "It's going to take a while to get over this."
Earlier in the day, Kyle Neuber scored the overtime winner as the Guelph Gryphons beat the UQTR Patriotes 3-2 for the bronze medal.