Nash, who is second in the League with 37 goals in the race for the Rocket Richard Trophy, sent the crowd home happy after skating toward the right circle before breaking into the middle of the ice and releasing a hard snap shot that found the left corner of the net to give the Rangers their sixth win in the past eight games (6-0-2).
It was his NHL-leading ninth game winning/game deciding goal of the season, which includes two in the tiebreaker this season.
"We've got the standings up in the dressing room so it's hard not to see [where we stand]," Nash said. "We're worried about ourselves, worried about our game and our process and our game plan."
Martin St. Louis had two goals and Kevin Hayes also scored for the Rangers, who (36-16-6) have now earned at least one point in 11 of the past 12 games (9-1-2). They trail the Metropolitan Division-leading New York Islanders by two points with three games in hand. The Islanders were shut out by the Vancouver Canucks in a 4-0 loss on Sunday.
"It's turning into playoff mode here; everyone is fighting," Rangers captain Ryan McDonagh said. "For us, we know what makes us successful. It's a matter of giving ourselves the best chance. This last stretch here, we've done a pretty good job of that."
In the tiebreaker, St. Louis scored in the first round and J.T. Miller hit the right post against Blue Jackets goaltender Curtis McElhinney in the second. Mark Letestu scored for the Blue Jackets in the first round and Ryan Johansen hit the crossbar before Cam Atkinson was stopped by Cam Talbot to seal the game, giving him his first career shootout win.
Talbot made 27 saves in regulation and overtime to improve to 6-1-2 since taking over for injured Henrik Lundqvist (neck) on Feb. 4.
"Cam can step up and fill that spot," Nash said. "You never want to see your leader (Lundqvist), your best player go down. But it gives a chance for the team to rally and step up their game."
Said McDonagh: "We had confidence in Cam and we had confidence in our system. There's no question that [Lundqvist] is a big part of our success but with Cam there, he is just as calm and composed. He has been in the structure for a while so he understands how we want to play and he has good chemistry with us defensemen."
The Blue Jackets (26-28-4), who closed out a five-game road trip 2-2-1, begin a three-game homestand against the Buffalo Sabres on Tuesday.
"You don't usually like to trade chances like that [in the third period] but we did a great job on the penalty kill [early in overtime] and had opportunities to win," Blue Jackets forward Brandon Dubinsky said. "I'm happy with the point, but obviously we wanted two. It's been a tough stretch for us, having four games in four tough buildings. We got in real late [Sunday morning from Montreal] and I think we were a little bit fatigued. But we kept fighting; it says a lot about our character in this room."
Columbus got goals from Marko Dano, Anisimov and David Savard. McElhinney, who was making his fourth straight start, made 34 saves. McElhinney was particularly sharp in overtime when he made six saves, but he credited Nash on the shootout winner.
"We've seen that move a bunch from him but elite players are able to execute similar moves over and over again, so credit to him to being able to pull it off," McElhinney said.
After spotting the Rangers a 3-0 lead, the Blue Jackets pulled even with three unanswered goals, the tying goal coming with 4:19 remaining in the third off a point shot by defenseman David Savard that deflected off the stick of Talbot and into the net. The Blue Jackets carried much of the play in the third, outshooting the Rangers 8-1.
"They are a desperate team and they competed real hard and we expected that and I didn't expect them to go away and they didn't," Rangers coach Alain Vigneault said. "We got two points and that's the most important thing."
The Blue Jackets scored twice in the second on goals by Dano and Anisimov. Dano made it 3-1 after taking a pass from Nick Foligno and sending a shot from the right circle for his second of the season at 2:17.
Anisimov, acquired by Columbus in the trade that sent Nash to the Rangers in the summer of 2012, scored his fourth of the season off a great individual effort at 18:11. With the Rangers defense backing up, Anisimov threw a backhand on net, then took another shot that was blocked before jamming a third attempt inside the right post.
St. Louis connected for his second goal 1:24 into the second to give the Rangers a 3-0 lead. McDonagh found St. Louis alone in the right circle and the veteran completed a nice passing play for his 18th of the season. It marked the first two-goal game by St. Louis since Nov. 3 in a 4-3 shootout loss against the St. Louis Blues.
"We talk all the time about trying to find ways," St. Louis said. "Obviously up three goals, [going to a shootout] is not the way you are trying to get two points. We should have pulled away and closed it out but at the end of the day you find a way."
Hayes and St. Louis scored in the first period to give the Rangers a 2-0 lead. Hayes opened the scoring when he took a pass from Carl Hagelin at the Blue Jackets blue line, skated uncontested down the middle of the ice and sent a shot over the glove of McElhinney at 5:57.
St. Louis made it 2-0 when he took a pass from Derek Stepan at the left post and scored at 8:06.
Blue Jackets defenseman James Wisniewski served as a healthy scratch for the first time since signing a six-year contract worth a reported $33 million in 2011. Coach Todd Richards inserted Jordan Leopold into the lineup, his first game since Feb. 9.
The Rangers play the second of a three-game homestand against the Calgary Flames on Tuesday.