Tim Taylor, Vincent Lecavalier, and Eric Perrin also scored for the Lightning, who have beaten the Flyers 10 straight times. R.J. Umberger and Randy Jones scored for the Flyers (3-8-1), who rallied from a 3-0 deficit with a pair of goals within 21 seconds in the third period.
Holmqvist had 30 saves, including solid stops on point-blank shots by Simon Gagne and Sami Kapanen in the first period. He also denied Peter Forsberg's redirection attempt late in the second.
Holmqvist was signed as a free agent by the Lightning on July 1. He came into the game winless in five career decisions, two this year and the other three with the New York Rangers over parts of three seasons.
St. Louis flipped the puck in from the slot to put Tampa Bay ahead at 10:39 of the first period after Lecavalier split two defenders with a pass from inside the blue line. St. Louis added his second goal in the second to make it 2-0.
Taylor scored on a scramble with 1:50 left in the second period, triggering a cascade of boos from the restless Philadelphia fans.
Umberger spoiled Holmqvist's shutout bid at 11:20 of the third period, beating the goalie to the stick side. Jones' goal came at 11:41 when his shot bounced off Tampa Bay defenceman Paul Ranger.
Forsberg was assessed a double minor for high-sticking and unsportsmanlike conduct, plus a 10-minute misconduct, at 15:50.
Lecavalier and Perrin scored empty net goals in the last two minutes.
Notes: The Flyers' last win against the Lightning was 4-1 on April 4, 2003, at Tampa Bay. ... St. Louis and Lecavalier each extended scoring streaks to seven games. St. Louis has eight goals and three assists in that span. Lecavalier, who also had two assists, has scored a goal in six straight games. ... Tampa Bay came into the game last in the NHL in penalty killing on the road but held the Flyers scoreless in five chances. ... The Flyers have yet to win two consecutive games this season.