St. Louis also set the previous mark against the Hurricanes, scoring three times in a 9:43 stretch of the first period in a 5-4 victory Jan. 15, 2004.
Ruslan Fedotenko and Vincent Lecavalier also scored for the Lightning, who have won four of five. Marc Denis made 23 saves.
Stanley Cup champion Carolina, 4-2-1 in its last seven games, got a short-handed goal from Eric Staal with 5:15 to play. Cam Ward was replaced by former Lightning goalie John Grahame after allowing four goals on 21 shots through two periods.
Tampa Bay took a 2-0 lead on St. Louis' power-play goal at 10:46 of the second. Brad Richards was in the left corner when he sent a pass off the end boards. The puck wound up trickling in front of the net to St. Louis.
St. Louis made it 3-0 on a rebound goal with 4:38 left in the second, and completed his fourth career hat trick from the right circle with 2:57 to go.
Fedotenko put the Lightning ahead 1-0 at 7:02 of the first. Lecavalier scored a third-period power-play goal.
Notes: Mikael Renberg is only other Lightning player to score three goals in a period. He did against Florida on March 21, 1998. ... Carolina D David Tanabe (upper body) missed his second straight game. Hurricanes D Niclas Wallin (lower body) sat out his third consecutive game.