Strong defense and more good goaltending helped the Rangers beat Columbus 4-0 and put the team in a playoff position.
Trocheck scored two goals on three shots and went plus-3 in Saturday's 4-0 win over the Blue Jackets.
The Rangers moved ahead of the Blue Jackets in the playoff standings as Shesterkin made 21 saves for the shutout.
Jonathan Quick will play his 19th NHL season after signing a one-year, $1.55 million extension with the Rangers.