"You have to have guts to do that move," said Jagr, penalized at the start of overtime for using an illegal stick. "In front of 20,000 people watching you, it's not that easy to do."
With only two healthy skaters left on the Rangers' bench, Malik -- a defenseman -- took a shot with his stick between his skates and beat Kolzig for the Rangers' fifth straight victory -- their longest winning streak in nearly four years.
"I was watching everything before me," Malik said. "Olie was unbelievable, he stopped everything from shots, moves. I just thought to myself, 'Maybe I'll surprise him.' I tried the move and it worked."
New York's five-game winning streak is its best stretch since a five-game run from March 30-April 8, 2002. The Rangers (16-7-3) are nine over .500 for the first time since the end of the 1995-96 season.
The Rangers, who also got shootout goals from Michael Nylander, Ville Nieminen and defenseman-turned-forward Jason Strudwick, improved to 4-1 in the new tiebreaker. Washington fell to 3-2 in shootouts despite goals from Andrew Cassels, Brian Willsie and Bryan Muir.
Nieminen and Strudwick both scored to keep the shootout going, with Nieminen countering Willsie's sixth-round goal and Strudwick matching Muir's 14th-round score.
"It was actually kind of fun," Kolzig said. "On this stage, Madison Square Garden, Saturday night ... If I stop Jason Strudwick, we win the game. I didn't expect Malik to pull a move off like that."
Chris Clark and Willsie scored second-period goals to rally Washington from a 2-0 deficit after Jason Ward and Jed Ortmeyer scored for the Rangers. It was the sixth straight meeting between the clubs decided by one goal.
Kolzig and Rangers counterpart Henrik Lundqvist were sharp in the third period and even better in the shootout.
"I started to think it would never end," said Lundqvist, who has slipped under the rookie radar with Capitals forward Alexander Ovechkin and Pittsburgh's Sidney Crosby stealing the headlines.
Kolzig turned away a good scoring chance from Jagr, his former teammate, in the third. The Capitals were waiting for the right moment to challenge the NHL's leading goal scorer's stick.
"We played with him for three years so we all knew," Kolzig said.
Lundqvist, subbing for injured starter Kevin Weekes, was the first to stop Ovechkin in a shootout.
"If I can get my stick to lift up the puck backhand, I can score," said Ovechkin, who said the ice made the puck bouncy. "It's my mistake."
Ovechkin, who leads rookie scorers with 15 goals, made the defensive stop of the game in regulation. Ortmeyer raced in on a breakaway with just over 10 minutes left, but Ovechkin dived in front to knock the puck away.
He needed just over six minutes to record his first shot after failing to get one for the first time in the NHL in a shootout loss to Tampa Bay on Wednesday.
Just like fellow No. 1 pick Crosby, Ovechkin got on the score sheet in his first trip to Manhattan. He earned an assist on Clark's sixth goal.
The Capitals, who held a 37-26 shots advantage, got even at 2 when Ovechkin's road roommate, Willsie, scored at 10:36. Clark scored Washington's first goal by deflecting in Ovechkin's shot.
The Capitals had the better of the play throughout the first period and were outshooting the Rangers 13-4 when Ward netted New York's first short-handed goal of the season on a breakaway with 2:44 left.
The Capitals power play continued to be a problem, going 0-for-7 including four chances after the second period. Washington entered with the NHL's third-worst unit, connecting just 15 times in 126 chances, and yielding five short-handed goals.
With the teams skating 4-on-4 to start the second period, Ortmeyer put in a rebound to make 2-0 just 14 seconds in.
- Rangers defenseman Fedor Tyutin returned to the lineup after missing four games with a fractured finger. Center Steve Rucchin sat out his second straight due to a lower back strain.
- The span of 7:04 between Washington's second-period goals was long by the Capitals' standards this week. Clark and Brooks Laich scored 14 seconds apart at Pittsburgh on Tuesday. Matt Pettinger and Brian Sutherby connected 13 seconds apart the following day against Tampa Bay.
- Rangers defenseman Tom Poti strained his groin and didn't play in the third period. He said he might have been able to go in the shootout if necessary.