Maltby, who scored just five goals in the regular season, also sent the game into overtime with his tally in the third period.
"I was disappointed in my season personally, but it was tough to be too down because we had such a great season," Maltby said. "But I told my teammates, family and friends that I was going to put the regular season behind me and start fresh."
In the second overtime, Mathieu Schneider dumped the puck into the Edmonton zone and the puck rolled around to Maltby at the right half wall. The gritty forward then quickly fired a wrist shot that hit off an Edmonton player in the right circle and through Dwayne Roloson's five hole to win it for the top- seeded Red Wings.
"My (goal) happened to just clip the defenseman's stick and went five hole on Roloson," added Maltby. "More times than not, those are the kind of goals that end up going in, in overtime. Good things happen when you get the puck to the net."
Game 2 is set for Sunday afternoon in Detroit.
Robert Lang scored the other goal for Detroit, while Schneider and Johan Franzen each added two assists in the win. Manny Legace was solid in goal with 23 saves.
Roloson did everything he could to give the Oilers a chance, as the goaltender made 54 saves in the loss. Sergei Samsonov had a goal and an assist while Chris Pronger also tallied for Edmonton.
"He (Roloson) played unreal tonight," said Ryan Smyth of the Oilers. "We've got to have everybody going and it starts from the goaltender out and he was that tonight."
The Red Wings were able to tie the contest at 2-2 with 6:17 left in the third as Maltby drove the net and had a rebound hit off the shaft of his stick and past Roloson. The play was reviewed to see if Maltby's stick was too high, but the goal stood.
With 1:50 left in regulation, Brendan Shanahan took a roughing penalty, giving the Oilers a power play and a chance to win it late. Edmonton failed to score as Legace made two saves in tight with about 20 seconds left in the third.
In the first overtime, Detroit carried the play with 16 shots unleashed on Roloson, who was up to the task and stopped them all. Edmonton was able to only get six shots on goal as the team was on the defensive for most of the session.
"Obviously when you lose it's not a great feeling," Smyth said. "That's why it's a seven-game series. The end result wasn't what we wanted but we've got to look forward to Sunday."
The Red Wings capitalized on an early power-play opportunity, taking a 1-0 lead 4:05 into the contest. Shanahan controlled the puck behind the cage after a shot from the point missed the net wide. Shanahan pushed the puck out to the slot to captain Steve Yzerman, who immediately tipped the disc to Lang at the right side of the crease and he slammed the puck past Roloson.
Edmonton tied the game with a power-play tally at 11:44 of the first. Ales Hemsky carried the puck up the right wing into the Detroit zone and from below the goal line centered the disc to a streaking Samsonov, who one-timed the feed past Legace low on the stick side in front.
Detroit controlled the majority of the action in the first with 15 shots compared to Edmonton's five.
The Wings continued to pile the shots on in the second, outshooting Edmonton 16-6, but it was the Oilers who scored to take a one-goal lead.
With 11:17 left in the second stanza, the Oilers went ahead 2-1, cashing in on the power play. Pronger took a pass from Jaroslav Spacek and moved to the middle of the point, ripping a slapshot through the five hole of a screened Legace.
Edmonton played strong defensively at the start of the third, limiting Detroit to just two shots on goal in the first 10 minutes of the period.
Detroit played without leading goal-scorer Pavel Datsyuk, who missed the game with a charley horse...Maltby now has 15 career playoff goals...Edmonton forward Ethan Moreau missed the game with a sore leg...Pronger's goal was his 11th career tally in the playoffs...Spacek had two assists.