Betts, who had just one goal in his previous 16 games this season, scored on an in-close redirection with 9:59 to play to give the Flyers a 3-2 lead. Richards extended the Philadelphia advantage to 4-2 at 17:22 of the third.
"I don't score too often, obviously," said Betts, who has 31 goals in 356 NHL games. "I've always said you need your third- and fourth-line guys to contribute offensively. For the most part we've been relying on too few individuals to carry the load."
Simon Gagne had a late empty-net goal for Philadelphia, which stopped a four-game losing skid and also picked up its fourth win in the last 18 games. Michael Leighton made 31 saves.
"When you get these, it's a minor step," Philadelphia coach Peter Laviolette said. "It's really important and the guys worked for it, especially in the third period. We need to follow it up with a whole bunch of big steps."
The Flyers have scored three goals or more just three times in the last 15 games.
Philadelphia's trip to Tampa got off to a strange start when Tuesday's practice was canceled because of a sewage line problem in their dressing room.
Tampa Bay got goals from Zenon Konopka and Victor Hedman. The Lightning, who have lost 11 of 14, were looking for their first three-game winning streak of the season.
"Unacceptable," Konopka said. "Painful. Frustrating. It's not good enough at all. We have the horses. If we continue on this road, we're not making the playoffs."
Betts put the Flyers ahead 1-0 on a fluke goal at 3:59 of the first. He was last Philadelphia player to touch the puck before Tampa Bay defenseman Andrej Meszaros accidentally sent it into his own net.
Richards made it 2-0 on his first goal in eight games, which came during a power play with 10:26 left in the first. The center assisted on Gagne's goal and has eight goals and 11 points in his last five games against Tampa Bay.
Konopka stopped a personal 61-game goal drought -- dating to Dec. 14, 2005 -- with a rebound goal to get Tampa Bay within 2-1 at 5:58 of the second. Hedman tied it at 2 from the top of the left circle with 7:58 remaining in the second.
"I think everybody is dejected," Tampa Bay coach Rick Tocchet said. "You've got to learn to win. Winning is very hard."
Flyers goalie Brian Boucher missed the game with a cut on his right ring finger. ... Tampa Bay rookie center James Wright was a healthy scratch. He has no points in his last 13 games and has gone 21 consecutive games without a goal. ... Flyers center Darroll Powe returned after missing 16 games with a left shoulder strain. ... Lightning defenseman Mattias Ohlund played in his 800th NHL game. ... Flyers defenseman Ian Laperriere assisted on both of Betts' goal for his first points in 23 games.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Tim Peel, Fred L'Ecuyer Linesmen: Jonny Murray, Pierre Racicot
Attendance: 16,177 (84.2% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Blair Betts (2)
Assists: Daniel Carcillo, Ian Laperriere
Mike Richards (14)
(Power Play) Assists: Simon Gagne, Chris Pronger
Zenon Konopka (1)
Assist: Steve Downie
Victor Hedman (3)
Assists: Kurtis Foster, Martin St. Louis
Blair Betts (3)
Assists: Oskars Bartulis, Ian Laperriere
Mike Richards (15)
Assists: Claude Giroux, Oskars Bartulis
Simon Gagne (2)
(Empty Net) Assists: Claude Giroux, Mike Richards