Riley Kieser, Nathan Burns, Jackson Houck, and Tristan Sieben also recorded a goal and an assist each for the Giants (2-4-0), while David Musil and Marek Tvrdon chipped in with two assists apiece.
Brett Kulak scored a single goal to round out Vancouver's offence.
Curtis Valk scored the lone goal for the Tigers (3-2-1).
Rookie goalie Tyler Fuhr stopped 20 shots in the win.
Marek Langhamer started in net for the Tigers but was chased after allowing three goals in just over five minutes of play. Dawson MacAuley finished the game, stopping 23 of the 26 shots he faced.
Kiesler opened the scoring at the 0:48 mark, converting the rebound of Austin Vetterl's initial shot.
Kulak, who also converted a rebound, made it 2-0 at 3:23.
Medicine Hat called a timeout after the second goal but it did very little.
Vancouver went to the power play and capitalized at 5:11 when Franson's shot through a screen squeaked through the pads of Langhamer.
Medicine Hat seemed to wake up a little after that but, when they did get opportunities, Fuhr stopped them.
Vancouver increased the lead to four when Burns took the puck hard to the net and Houck jumped on the rebound for his first of the season at 18:17.
Medicine Hat finally got on the board at 16:38 of the second period just as a power play expired. Valk deflected Kyle Becker's point shot past Fuhr.
Vancouver ended all hope of a Medicine Hat comeback when they scored twice in 14 seconds.
First Sieben recorded his second goal of the year when he deflected Musil's floater from the point at 4:36 of the third.
Then Tvrdon set up Burns for a one-timer at the side of the net.