Sam Reinhart scored for the Panthers, the No. 1 seed in the Atlantic and Presidents' Trophy winner for finishing with the best record in the NHL. Sergei Bobrovsky made 31 saves.
Florida, which averaged an NHL-best 4.11 goals per game this season, has scored three goals in this series.
"The will -- they're blocking shots, we're not, really," Panthers coach Andrew Brunette said. "They're managing different situations, and I think we've managed that fine, to be honest. But they've just got a little bit more will. When there's a loose puck, they're kind of outbattling us, and they want it a little bit more."
RELATED: [Complete Panthers vs. Lightning series coverage]
Game 4 is here Monday (7 p.m. ET; TNT, CBC, SN, TVAS). Teams that take a 3-0 lead are 197-4 (.980) winning a best-of-7 Stanley Cup Playoff series, including 1-0 in the first round this season (Colorado Avalanche defeated Nashville Predators).
Corey Perry gave Tampa Bay a 1-0 lead at 13:21 of the first period when he redirected a shot from Ryan McDonagh.
Reinhart tied it 1-1 at 16:07 when he scored the Panthers' first power-play goal this postseason, a one-timer from the slot off a pass from Jonathan Huberdeau. Florida had been 0-for-25 in the playoffs.
"It's tough not to get frustrated," Reinhart said. "I think there's certain things we're doing well, but obviously it's not enough bodies around the net picking up those loose opportunities. It's certainly frustrating when you're that close but you're not ultimately getting it in."