TJ Foster opened the scoring for the Oil Kings (27-9-5) early in the first period. He found a loose puck near the crease and wristed a shot off the cross bar into the net.
Jadon Descheneau's wrist shot beat the goalie high on the stick side as the Ice (16-24-1) tied the game late in the second period.
Leach's slapshot from the point gave Kootenay its final lead early in the third period with the Ice on a two-man advantage.
The Ice have won six games in a row and the Oil Kings had their winning streak end at four games.
Mackenzie Skapski made 31 saves for the win, while Laurent Brossoit stopped 31 shots for Edmonton.