Leafs starting goaltender Mikael Tellqvist had to be sharp early on, making three big stops seconds into a Jani Rita interference penalty. Ethan Moreau and Chris Pronger were denied on the chances.
At the other end of the ice, Conklin made a nice save stretching out his right leg to deny Staffan Kronwall on a one-time attempt.
After the Leafs killed off an Oilers penalty midway through the period, Bryan McCabe was sprung from the penalty box and sent in on a breakaway. Conklin stopped McCabe's breakaway attempt but Matt Stajan was standing right at the door step to put the rebound into the open cage.
Rita almost scored off the rush several minutes after the Leafs made it 1-0. He broke in on the right side and outmuscled Tomas Kaberle before being robbed by Tellqvist on a pad-stack save.
The Leafs netminder was brilliant again late in the period just as a Toronto penalty expired, denying Reasoner on a pair of point-blank scoring chances.
With time winding down in the first, Steve Staios was sent off on a questionable tripping minor. The result was a Leafs powerplay to close out the period, and the visitors took advantage.
Darcy Tucker from the right faceoff dot ripped one short side and high on Conklin to give the Leafs a 2-0 lead heading into the first intermission.
Shots on goal after one were 15-6 for Edmonton but thanks to some stellar play from Tellqvist, it was the Oilers trailing 2-0 on the scoreboard.
Some good hustle in the Toronto zone led to a great scoring chance in the slot by Shawn Horcoff
but his wrister was gloved down by Tellqvist.
Conklin came up big for Edmonton several minute later, getting a blocker down to stop Alexei Ponikarovsky.
Six minutes into the second on a delayed penalty, Hemsky, Horcoff and Smyth worked a nice three-way passing play but the Toronto netminder was able to stretch from post-to-post and keep it out.
Oilers penalty killers stepped up to the plate in the latter half of the second period. With the Oilers having to kill penalties to Matt Greene and Raffi Torres, the club limited Toronto to just two shots in the four minutes of power play time the Leafs enjoyed.
Late in the period, Marc-Andre Bergeron did a terrific job poking the puck away from Ponikarovsky as he and Jason Allison were breaking in on a two-on-one.
The play seemed to spark the Oilers, who scored with 22.4 seconds left in the period to draw within a goal. Bergeron fed the puck up ice to Hemsky who skated in behind the Leafs goal before centering it to Horcoff in front for the goal.
The Oilers dominated play once again in the second period, outshooting Toronto 11-5 and 26-11 in the game overall.
It didn't take Toronto long to regain their two-goal edge in the third period. 1:59 into the final frame, Clarke Wilm blasted a shot from the left faceoff circle that Conklin stopped but Chad Kilger was right there to pick up the rebound and raise it over Conklin.
With 8:54 to play and the Oilers needing a quick goal to get back into the game, Darcy Tucker took a hooking penalty but the power play was shortlived as Ryan Smyth
was sent off 15 seconds later for slashing Tellqvist.
With five minutes left in the third, Chris Pronger did a great job controlling the puck at the point as the Oilers cycled around the Leafs zone. His patience paid off in a fortunate bounce as his slap shot ricocheted off the end boards to Ryan Smyth
who put it in.
Jason Smith thought he had it tied up 30 seconds later but his blast was denied by Tellqvist as the Oilers continued to press for the equalizer.
Raffi Torres had a great chance to tie it up but was upended by Toronto defenceman Alexander Khavanov, putting the Oilers on a power play late in the period.
The hosts were unable to score on the man advantage, setting the stage for a frantic final minute. In the end, Edmonton could not solve Tellqvist to pull out the win.
Prior to the game, Walter Gretzky as well as the fathers of Darcy Tucker and Ryan Smyth
took part in the ceremonial opening faceoff. Edmonton Garrison was also represented in the faceoff... The Oilers went with the same lineup as Tuesday, with Jani Rita and Matt Greene drawing back in as well as Ty Conklin starting... Toronto went with the same team that played last night in Calgary, except Mikael Tellqvist got the start in goal... Horcoff extended his scoring streak to five games (3g, 4a).