Boyle pounced on a loose puck to score the tying goal in the third period and Richards scored 2:37 into overtime to give the Rangers a 4-3 win over the Tampa Bay Lightning on Thursday night.
"It's like other good teams that I've been on. There's never a panic in the locker room," Richards said. "We've been through it, and we've got a game plan. We've executed many times and we're very confident."
It could have been a discouraging night. The Rangers led for only 21 seconds, squandered several good scoring chances and lost Ruslan Fedotenko when he was hit on the chin.
New York coach John Tortorella said he did not have an update on Fedotenko's condition, and he did not want to talk about the hit. He had plenty to say about his team's resilience, though.
"I think it's a mindset. If you have some success, and we have had some success in the third period, you try to go back to that," Tortorella said. "We were playing well. They are such an opportunistic team, it doesn't take much for them to score goals."
Steven Stamkos demonstrated that by scoring his NHL-best 36th of the season near the end of a first period that had mostly favored the Rangers. Tampa Bay was outshot 10-4 in the first and 31-17 for the game.
The Lightning were coming off a loss at home to Los Angeles, but before that had points in seven straight games, including five wins.
"We came in against the No. 1 team in the conference and we made it hard for them again," Tampa Bay coach Guy Boucher said. "We've only lost one regulation game in nine games, so we are playing well. We're making it hard. We're fighting."
Derek Stepan scored and had an assist for the Rangers, who lead the Eastern Conference and have taken points in six of their last seven games.
On the winning goal, Richards rushed in to the left of goalie Mathieu Garon as Artem Anisimov carried the puck up the middle. He passed off, and Richards had to lunge forward to score, winding up on his knees as the puck went in.
Fedotenko left after he took a shoulder from Dominic Moore early in the third. Fedotenko spent about a minute face down on the ice, then was helped off. Moore was given a 2-minute minor for roughing.
Fedotenko's teammates didn't like the play.
"We're still pretty angry about that," said Boyle. "That was a really, really dirty play."
Boyle said Moore was upset about getting hit by Fedotenko earlier that shift and that the former Ranger was out of line for his retaliation.
"He should take a look in the mirror because that was garbage," Boyle said.
Bruno Gervais put the Lightning up on the power play at 12:26 of the second after the teams scored three goals in 75 seconds early in the period.
New York tied it when Ryan Callahan converted on a power play 4:33 into the period, and Stepan gave the Rangers the lead at 5:27. It lasted all of 21 seconds.
Vincent Lecavalier was stopped on the doorstep by Martin Biron, but the goalie had to venture out past the left post and Callahan filled the net, making him a target for Lecavalier to shoot at. Lecavalier bounced the puck off Callahan and in to tie the game.
"Obviously, it's not perfect for 60 minutes, but the results are there," Biron said. "We just have to tighten up a couple of things and move forward."
The Rangers had three good chances to tie it. There was a scrum in the crease in front of Garon that prompted a video review, but no goal was given. Later, with about 5 minutes left in the second, Marian Gaborik picked out Anisimov racing right at the net, but the shot went wide. About 2 minutes after that, Ryan McDonagh slapped a one-timer wide.
Stamkos put Tampa Bay up 1-0 on a diving, backhanded goal at 18:56 of the first. After a turnover, Stamkos sliced in on Biron at a steep angle, then tucked the puck between the goalie's legs while nearly horizontal.
Biron made 14 saves in place of Henrik Lundqvist, who had started every Rangers game against Tampa Bay since November 2005.
ESPN's Erin Andrews was shown on the scoreboard during a stoppage in the second period. When she heard cheers, she looked up and gave a sheepish grin and wave. ... Rangers D Steve Eminger returned after a shoulder injury and started the game as part of the first pairing. ... New York D Michael Del Zotto had two assists, giving him five points in the last six games. ... Tampa Bay was outshot 10-3 in the third period and overtime.
Information from ESPNNewYork.com's Katie Strang and The Associated Press was used in this report.