Chris Kreider and Ryan Carpenter also scored and Igor Shesterkin made 31 saves for the Rangers who snapped a three-game home losing streak. The Rangers are 13-1-2 in their last 16 games against the Coyotes, dating back to March 2014.
Goodrow broke a scoreless tie when he intercepted a misplayed puck in front of Ingram and deposited his fourth goal of the season at with just under five minutes remaining in the middle period.
Fox made it 2-0 just 1:18 later with his fifth goal after the Coyotes had more chances for much of the first two periods. Artemi Panarin had his team-leading 17th assist on the play, giving him 22 points on the season.
Chris Kreider extended the lead with a power-play goal at 4:39 of the third for his seventh of the season. Mika Zibanejad and Fox had assists, stretching Fox's point streak to six games and giving Zibanejad a point in eight of his last nine.
Keller spoiled Shesterkin’s shutout bid with his sixth of the season on the power play at 8:33 of the third, extending his point streak to five game and giving him a team-leading 17 points.
Carpenter made it 4-1 at 11:43 with his first goal since joining the Rangers in the offseason.
Both teams were coming off losses the previous night — the Rangers lost 2-1 at Nashville and the Coyotes were beaten 4-2 at New Jersey.
Ingram was sharp in the first half of the game, stopping Ryan Lindgren on a 2-on-1 short-handed break 12 minutes into the first on the Rangers’ initial shot on goal after Arizona recorded 10 against Shesterkin.
Ingram also denied Zibanejad's one-timer on a Rangers power-play with just under two minutes left in the first.
LONG TRIP/ARENA DRAMA
Arizona’s road trip is tied for the longest in league history and is occurring while annex construction of Mullett Arena at Arizona State University is completed. The Coyotes relocated to the 5,000-seat college-campus arena while seeking approval for a permanent home in Tempe, Arizona, where the Coyotes have been negotiating to build on a tract of land just west of downtown. Arizona was playing on an annual lease at Gila River Arena until the city of Glendale said it would not renew the lease. The Tempe city council voted unanimously last Thursday to send a proposed arena and entertainment district to referendum in May.
Coyotes: At Vegas on Thursday night.
Rangers: At Seattle on Thursday night to start a four-game West Coast trip.
AP NHL: www.apnews.com/hub/NHL and www.twitter.com/AP_Sports
Allan Kreda, The Associated Press