Perry tied it 1-1 at 14:08 with a power-play goal. He redirected a shot by Namestnikov that hit off Tarasov and trickled across the line.
"You knew they were going to come out hard with their home opener, and you knew their juices would be flowing for them," Perry said. "And the crowd was into it early. They got an early [goal], but we found a way on the power play to get one right back."
Stamkos gave Tampa Bay a 2-1 lead at 15:21 when his shot from the right corner deflected in off the skate of Blue Jackets defenseman Adam Boqvist.
Nyquist scored 34 seconds later on a 2-on-1 to tie it 2-2, but Colton put the Lightning back in front 3-2 at 18:55.
"We had some juice early on, but how we played tonight, we were really sloppy," Columbus coach Brad Larsen said. "We weren't good enough tonight."
Cal Foote made it 4-2 at 7:45 of the second period, redirecting a return pass from Colton that deflected in off Blue Jackets defenseman Jake Bean's skate.
"We had some bad bounces, but that's not why we lost tonight," Larsen said. "They were the better team, plain and simple."