Callahan had two goals, and New York scored three times within 2:02 late in the second period of a 4-1 victory over the Ottawa Senators on Tuesday night.
Callahan, a member of the U.S. team that won the silver medal in Vancouver, scored 22 seconds into the second to tie it at 2. He added his second of the game during the Rangers' three-goal outburst late in the middle period, which chased Ottawa's Brian Elliott from the net.
"I think right when I jumped on the ice I was still competing at that speed and that level, and I found it helped me out a lot," said Callahan, who had one assist in six games at the Olympics. "I think that's one of the biggest things I tried to bring back, was not to have that sudden letdown where you don't keep your speed up and your game up, and I think that was one of the reasons I was successful tonight."
Henrik Lundqvist made 24 saves for New York, which has won three in a row.
"I just thought we stayed with it," Rangers coach John Tortorella said. "Even though we were down 1-0 -- the first shot goes in -- I thought we played a good first period. I thought we were pretty good through the neutral zone, our forechecking was coming, we give up an odd-man rush that cost us but we stayed with it and continued to just try to play a simple game.
"Some guys contributed, I thought our defense got the puck up to the forwards and we found our way."
Milan Michalek scored his 21st for Ottawa, which entered the break in first place in the Northeast Division. The Senators had won 14 of 16 games, including a team-record, 11-game winning streak that began with a 2-0 victory in New York on Jan. 14.
"There were some turnovers and they were coming back the other way and driving the net," Ottawa center Mike Fisher said. "A couple of bounces and some nice plays and it was in the back of our net a number of times. We've got to be better mentally and not let that happen again."
Elliott stopped 12 of 16 shots. Pascal Leclaire replaced him after Avery's goal and made nine saves the rest of the way.
Marian Gaborik missed the game due to an unspecified lower-body injury. Gaborik, who leads the Rangers with 35 goals and 69 points, missed two of New York's last three games before the two-week break and was limited to four total minutes due to a cut on his right knee.
The Slovakian right wing played through that injury during the Olympics and had four goals and one assist in seven games, including Slovakia's loss to Finland in the bronze-medal game Saturday.
A highlight package of various Canadian Olympic successes was shown on the video scoreboard during the singing of The Star-Spangled Banner prior to the game. Images of Sidney Crosby's overtime goal in Canada's gold medal win over the U.S. in the men's final drew cheers.
"I didn't see it," Callahan said. "I was on the ice. When the anthems are on I'm looking at the flags."
A Senators spokesman said the timing of the video's showing was a technical mistake.
"I thought they should have saved it for 'O Canada' to show that," Rangers defenseman Wade Redden said. "I was surprised they did it and figured it had to be a glitch on their part."
Michalek opened the scoring 3:51 in when he took Jason Spezza's cross-ice pass and drove a one-timer past Lundqvist.
Callahan drew the Rangers even at 1 early in the second when he drove down the left side and slipped past Ottawa defenseman Matt Carkner to put a shot past Elliott for his 16th goal 22 seconds in.
Dubinsky put New York ahead at 15:44 and Callahan made it a two-goal lead with his second of the game 1:12 later.
Avery scored the Rangers' third goal in 2:02 at 17:46 to end Elliott's outing.
Rangers captain Chris Drury was also a member of the U.S. Olympic team. Tortorella was an assistant coach. ... Rangers D Michael Del Zotto (upper-body injury) also missed the game. ... The Rangers' record for fastest three goals is 28 seconds, set by Doug Sulliman, Eddie Johnstone and Warren Miller in the first period of a 6-6 tie against the Colorado Rockies on Jan. 14, 1980. ... Senators D Filip Kuba suffered a lower-body injury in the first period. He left the game and did not return.