Reilly completed 22-of-30 passes for 326 yards as the Eskimos improved to 2-1 on the season, while the Lions are 1-1.
The Lions started the game with a single on a 37-yard missed field-goal attempt by Tyler Long.
B.C. got the ball back when Reilly was picked off by T.J. Lee, eventually leading to a one-yard touchdown plunge by Jeremiah Johnson.
Edmonton continued to implode, fumbling the ball away to Dyshawn Davis on its own 23-yard line on the ensuing kick-off. Long kicked a 14-yard field goal to put the Lions up 11-0 midway through the first.
The Esks got on the board when B.C. conceded a safety.
Long started the second with 39-yard field goal, but then hit the uprights on his next attempt.
Edmonton finally got its offence going late in the second, when Reilly found Natey Adjei for a 14-yard passing TD. Then he hit Kenny Stafford for a 13-yard strike through the air with just 30 seconds left and added a two-point convert pass to Duke Williams to take a 17-14 lead into the half.
The Esks picked up where they left off in the third, with a three-yard TD run by C.J Gable, although the convert kick failed.
Edmonton's momentum remained late in the third when Reilly completed a 64-yard pass-and-run into the end zone to Williams, who also caught another two-point convert.
The Lions finally ended Edmonton's run of 29 straight points with a one-yard TD by backup QB Cody Fajardo to start the fourth.
Edmonton bounced back with a one-yard rushing major of their own by Reilly.
The Eskimos added a late Sean Whyte field goal.
Both teams are back in action again next Saturday, as the Lions head to Winnipeg and the Eskimos are in Toronto.
Notes: Lions defensive end Odell Willis made his return to Edmonton after being traded away in the off-season. Willis played for the Eskimos for five seasons ... B.C., with former Edmonton GM Ed Hervey in charge, has nine former Eskimos on its roster.