Boughner, who had been an assistant with the Sharks, was promoted after coach Peter DeBoer was fired on Wednesday.
San Jose, trying to end a five-game winless streak (0-4-1), has been outscored 22-7 during the skid.
Joe Thornton will become the 12th in NHL history to play in 1,600 regular-season games; The 40-year-old center will join forward Patrick Marleau (1,686 games played) as the first teammates in League history to appear in the same game with each having reached the 1,600-game plateau.
The Rangers seek their seventh victory in 11 games; they're 6-3-1 in their past 10 after going 2-3-1 in their previous six.
Goalie Alexandar Georgiev will start; he's 4-1-0 with a 1.81 goals-against average and .954 save percentage in his past five starts.