Cheek took a perfect cross-ice pass from Blake Orban following a turnover and slid the puck under goalie Mac Engel with less than six minutes to go in the third.
It was Cheek's second goal in as many games since being acquired by the Giants in a trade last week.
Nathan Burns and David Musil scored for Vancouver (1-3-0), who was the last winless team in the WHL. Brett Kulak had two helpers. Cheek also had an assist.
Mike Aviani and Mitch Holmberg tallied for Spokane (2-1-0).
Spokane defeated Vancouver 4-2 in the first round of last spring's playoffs.
Tyler Fuhr (1-0-0) looked very overwhelmed and nervous in his first WHL start but made 13 saves for the win, including two big ones in the final couple minutes.
Engel (1-1-0) stopped 21 shots in the losing effort.
Spokane opened the scoring on the game's first power play at 4:29. During a slow developing odd-man rush Aviani was sent in alone by Jason Fram's pass and the Surrey, B.C., native used a nifty backhand deke to beat Fuhr for his third goal of the season.
Burns' third of the season tied the game with a little more than two minutes to go in the opening frame. While on the power play, Burns took a cross-ice feed from Cheek and wired a shot from the face-off dot just under the crossbar.
Musil gave Vancouver a 2-1 lead six minutes into the second period. He took a pass from Kulak, walked to the top of the face-off circle and squeezed a wrist shot through Engel's equipment for his first of the year.
Engels made two big stops in the second to keep his team within one. First he stopped Marek Tvrdon on a two-on-one, and then with six minute left in the period he robbed Tristan Sieben on a partial breakaway.
Holmberg tied the game for Spokane at 7:59 of the third. After Fuhr stopped Brenden Kichton's initial shot, Holmberg beat the defender to the rebound and quickly backhanded the loose puck under the bar for his fifth of the young season.
The Giants regained the lead on a turnover at the blue-line at 14:07 of the third. Tvrdon poked the puck to Orban who rushed down the right wing before centring to Cheek for the winner.