Columbus, the NHL's third-worst team (24-32-6), shook off an early 2-0 deficit and snapped its three-game losing streak by taking advantage of the Rangers when they were in position to take control of a crucial contest.
Anders Eriksson scored a rare goal late in the first period, and Chimera and Nash added goals minutes apart in the second to give the Blue Jackets their 10th road victory and first ever in Madison Square Garden (1-1-1-0).
Fredrik Norrena (16-14-3), on pace to be Columbus' first goalie to finish a season over .500, made 40 saves - including 17 in the third period. He turned away the Rangers during a late power play and then blocked a hard, bouncing puck with under four minutes remaining.
The Blue Jackets had scored just four short-handed goals this season, and the Rangers had allowed an NHL-low two.
Blair Betts and Jaromir Jagr staked New York to its early lead but the Rangers failed to gain any ground in the Eastern Conference playoff race. They are in 12th place, six points below the postseason cutoff with only 20 games remaining.
Henrik Lundqvist stopped 22 shots but allowed more than two goals for the fourth time in 18 games.
The Rangers came out flying and showed no hangover from their emotional, hard-hitting home-and-home series with New Jersey in which they earned only one point.
Betts and Jagr provided New York with a 2-0 lead just 5:11 in and before Columbus recorded a shot on Lundqvist.
Betts scored his seventh of the season during a fine shift from the Rangers' rugged fourth line. Ryan Hollweg and fellow enforcer Colton Orr each earned their first assists of the season at 2:46.
Jagr, still hearing criticism for not taking part in the shootout Thursday night in the loss to the Devils, heard plenty of cheers when he scored his 22nd goal 2:25 later. It was only Jagr's fifth power-play tally after netting a team-record 24 last season.
The shots were 6-0 and Norrena stood in his crease with slumped shoulders and took deep breaths as the Rangers celebrated.
Columbus, 2-7-1 in its previous 10 games, took over soon after, prompting the New York fans to boo the home team off the ice after the final two frames and when the three stars of the game were announced.
The Blue Jackets, who entered with the third-fewest road victories in the league, started to chip away when Eriksson let a shot go from inside the blue line that caromed through traffic and got by Lundqvist with 1:24 left in the first period. It was the defenceman's first goal in 60 games, dating to April 3, 2004.
Chimera and Nash then took advantage of New York's power-play unit, which has connected for goals in 11 of 13 games.
Chimera barrelled through New York's defence and scored an unassisted goal at 11:02. Nash gave the Jackets the lead 4:52 later.
Notes: It was Columbus' first Garden visit since Dec. 3, 2002. ... Rangers D Aaron Ward was a healthy scratch. ... Columbus D Bryan Berard, who has fallen out of favour with coach Ken Hitchcock, also was benched. ... Rangers forward Martin Straka left with an upper-body injury in the second period.