Henrik Lundqvist started and lost the first two games (3-2 and 4-1) of the series, with Shesterkin deemed unfit to play.
Shesterkin, 24, made his NHL debut in January and played a massive role in the Rangers' second-half surge up the Eastern Conference standings. Shesterkin went 10-2 in 12 starts with a .932 save percentage and 2.52 goals against average.
Puck drop for the critical contest is scheduled for 8:00 p.m. ET.