Jason Ward and Michel Ouellet also scored for the Lightning, who tied a franchise record set in 2002 by starting the season 5-0 at home. Tampa Bay is also 12-1 against the Flyers since the start of the 2003-04 season.
Philadelphia got goals from Jeff Carter and Mike Knuble. The Flyers played without left wing Simon Gagne (dizziness) and defenceman Derian Hatcher (sore right knee). Gagne, hit in the head by a shot in Wednesday's 4-3 loss at Florida, might return this weekend.
Prospal made it 3-1 during a power play at 3:38 of the second. He redirected Richards' pass past backup goalie Antero Niittymaki, making his first start this season.
Knuble cut the Flyers' deficit to 3-2 at 3:46 of the third. Philadelphia has lost two in a row after starting the season by winning six of seven.
After a Philadelphia turnover, Ouellet scored to put Tampa Bay ahead 4-2 with 6:34 left in the third. Richards scored an empty-net goal with 1:11 remaining.
Tampa Bay took a 2-1 lead after the first on goals by Ward and Richards, who scored during a power play. Carter picked up his sixth goal this season midway through the period.
Notes: The two goals allowed by the Flyers in the first was just second time in 19 periods Philadelphia had given up more than one goal. ... Lightning C Vincent Lecavalier, who led the NHL with 52 goals last season, got a fighting major for the second consecutive game.