Grebeshkov scoring 3:25 into overtime as the Oilers won their second in a row to start the pre-season, defeating the visiting Toronto Maple Leafs 3-2 in front of a sellout crowd of 16,839.
Grebeshkov, who spent last season playing in Russia before being acquired by the Oilers from the Islanders in exchange for Marc-Andre Bergeron, took a Shawn Horcoff feed and fluttered a shot past Leafs starter Justin Pogge to secure the win.
Oilers head coach Craig MacTavish says the whole organization is still discovering what the 23-year-old defenceman brings to the table.
"He has all kinds of skill," he said of Grebeshkov. "For him to win the hockey game has to be a good feeling for him. There were other aspects of his game that we all saw can use some fine-tuning but there is obviously a lot to work with there."
Horcoff had a goal and two assists, while Viacheslav Trukhno also scored for the Oilers.
"It was just one of those games where things went in for me," said Horcoff. "I put the work in during the off-season. I feel good and ready to go. I'm trying to use these games to get my timing and speed up. For the first one that was OK but the games will get tougher."
Alexei Ponikarovsky and Brian McCabe replied for the Maple Leafs, playing their first exhibition match of the year.
Veteran Darcy Tucker says it wasn't the start that the Leafs were looking for.
"It wasn't the pace that we wanted and it definitely wasn't the finish to the game that we wanted," he said. "We need to get better."
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.