Stu Barnes also had two assists and scored the winning goal for the Panthers--their first victory in a home opener for the third-year franchise.
The victory was bittersweet for fans, though, as Florida owner Wayne Huizenga has said he may move the team out of state next season if the Panthers can't get a new lease at the Miami Arena.
Calgary's Theoren Fleury had a goal and two assists for the Flames.
Yzerman continued his pattern of successful performances in Edmonton. In 34 games against the Oilers, he has 29 goals and 26 assists.
The Red Wings broke the game open with two goals 13 seconds apart in the third period. Yzerman set up forward Tim Taylor at 6:01 when they were left unattended in front of the Edmonton net.
Detroit defenseman Nicklas Lidstrom scored his second of the season at 6:14 to seal the win.