Marian Gaborik added an empty-netter with a minute left, and Henrik Lundqvist made 19 saves for the Rangers, who earned their fifth win in six games (5-0-1). It was New York's first win this season when trailing after two periods.
"We knew the third period had to be our best," Staal said. "We need the points, obviously, more than they do. We came out and had a great period and did it again. It was a big win."
The Rangers moved into a points tie with eighth-place Philadelphia in the Eastern Conference playoff race. The Flyers have the tiebreaker edge because they have two more wins than New York. Both teams have four games remaining -- including a home-and-home series to close the regular season next weekend -- and trail No. 6 Boston by two points.
New York is 20-15-4 on the road this season, but only 16-17-6 back home in Madison Square Garden.
"We've been a good road team all year long," Rangers coach John Tortorella said. "We wouldn't be in this situation if we handled ourselves a little bit better at home. We can't look back. ... We need to look ahead and stay consistent no matter where we're at right now."
Keith Ballard scored the lone goal for Florida, which carried a 1-0 lead into the third. The loss eliminated the Panthers from postseason contention. The Panthers haven't been to the playoffs since the 1999-2000 season.
"We knew where we stood," Ballard said. "We've put ourselves in this position."
Scott Clemmensen stopped 23 shots in his second straight start. Clemmensen made 36 saves in a 1-0 Florida win over Boston on Thursday, a game in which Ballard also had the only goal.
New York, playing the second game of back-to-back contests, was coming off a 5-0 win over Tampa Bay on Friday.
Prust put the Rangers up 2-1 at 9:36 in the third period when he poked in the puck, sending it off the post to give New York its first lead. The Rangers stretched the advantage to 3-1 at 11:06 when Drury swept in rebounding puck.
"We weren't happy with our first two periods. We were just average," Prust said. "We were sitting on the bench and said, 'Let's get going.' In the third period we were able to get in deep and do what we usually do, just kind of crash and bang and throw pucks to the net and it paid off."
Staal tied it 18 seconds into the third with a quick shot from about 10 feet inside the blue line that went high over Clemmensen's glove side, making it 1-1. The defenseman scored for the third straight game, giving him eight goals on the season. Lundqvist earned his first assist of the season and fifth of his NHL career.
"That's exactly what they needed to get back in the game," Panthers coach Pete DeBoer said. "The momentum obviously shifted on that play. We couldn't get it back."
Ballard opened the scoring at 6:38 of the second period with his third goal in four games. He took a pass from Shawn Matthias and beat Lundqvist with a shot from above the left circle that bounced off the crossbar and in.
Gaborik sealed the Rangers' win with his 41st goal. Gaborik, who also earned an assist on Drury's goal, tied his career high with 83 points.
Rangers C Olli Jokinen, former captain of the Panthers, played in South Florida for the first time since the 2007-08 season. ... Rangers LW Sean Avery (knee), C Brian Boyle (foot) and RW Ryan Callahan (leg) were scratched. ... Florida recalled RW Mike Duco and D Clay Wilson from Rochester (AHL). ... Rostislav Olesz (hand) returned to Florida's lineup after missing two games. ... The Rangers and Panthers had a combined 10 shots on goal in the scoreless first period.
Copyright by STATS LLC and The Associated Press
Arena: BB&T Center Location: Sunrise, Florida
Referees: Greg Kimmerly, Dan O'Halloran Linesmen: Scott Driscoll, Thor Nelson
Attendance: 18,011 (93.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Keith Ballard (8)
Assists: Shawn Matthias, Radek Dvorak
Marc Staal (8)
Assist: Henrik Lundqvist
Brandon Prust (4)
Assists: Jody Shelley, Michael Del Zotto
Chris Drury (13)
Assists: Aaron Voros, Marian Gaborik