Dion Phaneuf scored his first goal of the season to put the Leafs ahead 1-0, and Jean-Sebastian Giguere had 23 saves in the opener of the three-game swing through western Canada.
Eberle's goal tied the game 1-1 at 11:45 of the first period, but Giguere had things under control the rest of the way. Edmonton had 12 shots in the first period but managed only three in the second period and nine more in the third.
Mikhail Grabovski's power-play goal with 2:22 left in the opening period gave the Leafs the lead for good.
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