Grebeshkov, acquired last season from the New York Islanders, took a Shawn Horcoff feed and fluttered a shot past Leafs goalie Justin Pogge to secure the win in front of a sellout crowd of 16,839 at Rexall Place.
Viacheslav Trukhno and Horcoff also scored for the Oilers.
Alexei Ponikarovsky and Brian McCabe replied for the Maple Leafs, playing their first exhibition match of the year.
The two teams traded power-play goals late in the first.
Edmonton’s Trukhno picked up a rebound at the side of the net on a two-man advantage and beat Pogge just past the 15-minute mark.
Less than two minutes later, Darcy Tucker sent Ponikarovsky in on a breakaway and he wristed a shot past Oilers netminder Mathieu Garon to tie the game 1-1.
Toronto took the lead three minutes into the third as McCabe blasted a slap shot up high past replacement goaltender Devan Dubnyk, another power-play goal.
Edmonton responded five minutes later. Shawn Horcoff found a loose puck in a scramble in front of the Leafs net and set a backhand shot through Pogge’s legs to knot the game 2-2 and send it into overtime.
Notes: Forward Anson Carter played his first game in an Oilers jersey since coming to the team on a training camp audition last weekend, but left the game with a concussion in the first period. The 33-year-old Toronto native, who has played for eight NHL teams, last suited up for the Oilers in the 2002-03 season. . . . Edmonton also lost defenceman Mathieu Roy in the first after he took a Jeremy Williams shot in the face. . . . The Oilers unveiled their impressive new locker-room at Rexall Place on Monday. The new 930-square metre expansion project cost $3.5 million.