"It should be that way," Richards said. "Last year we struggled at home for some reason, but it should be this way. Our team is built to play that uptempo style, and we've done that this year. We're taking care of business here."
"Kept things going on a good roll here on home ice, which is very important I think," Richards said. "We want to establish ourselves in this building."
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 defenseman 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.
"We've got to regroup," Flyers coach John Stevens said. "There's no time to feel sorry for ourselves. We knew it was going to be tough going on the road, playing teams that are fighting and scratching to get off to a good start."
The Flyers are two games through an eight-game road trip.
"Maybe guys were a little bit too comfortable," Knuble said. "So now maybe guys are a little bit on guard and a little bit frustrated. It will be good going into Boston [Saturday]."
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.
"A key part of our game tonight was other guys scored, other guys were making big plays other than our top line," Lightning coach John Tortorella said.
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. ... Tampa Bay LW Jan Hlavac had three assists.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Kevin Pollock, Justin St. Pierre Linesmen: Scott Driscoll, Jay Sharrers
Attendance: 18,616 (96.9% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Jason Ward (2)
Assists: Filip Kuba, Jan Hlavac
Brad Richards (4)
(Power Play) Assists: Chris Gratton, Jan Hlavac
Jeff Carter (6)
Vinny Prospal (8)
(Power Play) Assists: Brad Richards, Vincent Lecavalier
Mike Knuble (3)
Michel Ouellet (1)
Brad Richards (5)
(Empty Net) Assists: Jan Hlavac, Paul Ranger