Garand got the shutout in his fourth NHL game. He went 2-0-1 in three games late last season for New York, which was playing its third game in four nights to open the season.
Sean Durzi and Eeli Tolvanen scored to help New York (2-1-0) win for the second straight night after a 5-1 win against the Tampa Bay Lightning on Thursday.
John Gibson made 19 saves for the Red Wings in their season opener.
The Rangers took a 1-0 lead on a power-play goal by Durzi at 5:12. It was the defenseman’s first goal with New York after being traded from the Utah Mammoth on July 1 as part of the Vincent Trocheck deal.
Durzi appeared to score a second power-play goal at 7:10, but it was overturned after the Red Wings challenged for offside.
Red Wings defenseman Anton Johansson, making his NHL debut, hit the post later in the first period.
The Red Wings had 20 shots through two periods but managed only two in the third.
Tolvanen scored his second goal of the season into the empty net at 18:44 for the 2-0 final.
