Martin Gernat, Ashton Sautner, Dylan Wruck and Travis Ewanyk also scored for the Oil Kings, who host Game 5 on Friday.
Calder Brooks, Brooks Macek and Elliott Peterson scored for the Hitmen.
Laurent Brossoit made 22 saves for Edmonton, for his 10th win of the post-season.
Calgary's Chris Driedger stopped 12-of-17 shots, while Mack Shields allowed two goals while facing 22 shots.
Foster opened the scoring for Edmonton at 1:15 of the first period and scored 55 seconds later with the Oil Kings enjoying a two man advantage.
Gernat and Sautner put Edmonton up 4-0 before Brooks scored a power-play goal for the Hitmen.
Ewanyk added a late goal in the opening period to make it 5-1 Edmonton.
Macek scored on a penalty shot for Calgary at 7:56 of the second period.
After Wruck scored to give the Oil Kings a 6-2 lead, Peterson responded for Calgary before the end of the second.
St. Croix rounded out the scoring at 1:30 of the third period.
The Oil Kings were 1 for 6 with the man advantage, while the Hitmen scored once on eight power-play chances.Suggest a correction