Aaron Ward also had a goal and two assists for the Rangers, who improved to 3-1 on the road as they opened a four-game West Coast trip. Brendan Shanahan scored his team-leading ninth goal for New York.
Rookies Matt Jones and Patrick Fischer scored their first NHL goals for Phoenix, which has lost five of its last six games. Fischer is a 31-year-old centre who played 13 years in his native Switzerland.
Jones' goal came at 2:18 of the first period and gave the Coyotes a 1-0 lead. But that only woke up the Rangers, who dominated the rest of the way.
New York tied it 1-1 on Straka's fifth goal of the season at 10:06. Michael Nylander made a crisp cross-ice pass to Straka, who was all alone on the left post and flipped the puck past goaltender David LeNeveu.
The Rangers put the game away with four goals in a 10:33 span of the second period. They led 2-0 when Matt Cullen scored at 1:13 of the second period.
Then Jagr scored a trademark goal, swatting in a rebound of Ward's shot at 4:23.
Straka's second goal of the night came when LeNeveu left a rebound in the crease. Straka plucked it out of a crowd and backhanded it into the net, giving the Rangers a 4-1 lead.
New York made it 5-1 on Petr Prucha's second goal of the season, at 11:46.
The Rangers outshot Phoenix 14-7 in the first period and 16-7 in the second.
New York put the game away on Ward's goal at 4:32 of the third period, his second of the season.
Notes: Phoenix coach Wayne Gretzky faced his former team for the first time. Gretzky spent the final three seasons of his career with New York, retiring in a Rangers sweater in April 1999. ... The Rangers made their first trip to the desert since Dec. 29, 2003, when they beat Phoenix 3-2 in overtime. ... Coyotes RW Shane Doan (back) was scratched for the second consecutive game. ... Referee Don Koharski left the game in third period after being hit in the face with a puck.