The 18-year-old goaltender finished the first-round series with a 4-1 record, to go with a 1.91 goals-against average and a .942 save percentage.
Jake Virtanen and Elliott Peterson both had their first WHL playoff goals for the Hitmen, while Victor Rask also scored.
Coda Gordon scored the lone goal of the game for the Broncos, who failed to qualify for the WHL playoffs in each of the past two seasons.
Eetu Laurikainen made 23 saves in the Swift Current net in a losing cause.
The Broncos went 1 for 6 on the power play, while the Hitmen failed to score on three chances with the man advantage.
The Red Deer Rebels and Medicine Hat Tigers have also advanced to the second round of the playoffs in the Eastern Conference, while the Edmonton Oil Kings currently have a 3-1 lead over Kootenay Ice with Game 5 slated for Friday night in Edmonton.
Swift Current jumped out to a 1-0 lead thanks to a power-play goal by Gordon at 11:24 of the first period. Less than five minutes later, Virtanen drove hard to the net and snuck a shot through Laurikainen’s legs to pull the Hitmen even.
Shortly after Rask put the Hitmen up 2-1 at 12:07 of second period, Peterson added an insurance marker.
Although Swift Current outshot Calgary 13-8 in the third period, the Broncos failed to put any more pucks past Driedger, who was named the game’s first star.