Erne scored into an empty net from deep in the opposite end to make it 3-1 at 16:22.
"I just shot it down there," Erne said. "I'd love to say that was all skill, but there was maybe a little luck mixed in."
Point brought Tampa Bay to within 3-2 at 17:34 with a backhand in front of the net with the Lightning again having the extra attacker, but Perron scored the Red Wings' second empty-net goal with 25 seconds left for the 4-2 final.
"I thought we were good in the third," Point said. "We had a lot of chances, a lot of puck possession, we started shooting the puck more and creating those shot-scramble situations."
NOTES: Defenseman Filip Hronek had two assists and set a Red Wings record with an 11-game season-opening road point streak. He has 14 points (four goals, 10 assists) during the streak. Sergei Fedorov had a 10-game streak (19 points; nine goals, 10 assists) to begin 1993-94. ... Detroit center Andrew Copp had two assists, giving him five points (goal, four assists) in the past four games. ... Stamkos has 17 points (seven goals, 10 assists) during an 11-game point streak. ... Point had a game-high nine shots on goal.