Grove took the lead after 10 minutes when Dave Walker sent the ball through for Tom Urwin to fire into the top corner.
Walker added the second midway through the first half following Nick Ward's pass.
Substitute Liam Shotton set up Walker for Grove's third on 58 minutes and after Simon Bolland (75) had reduced Shepshed's deficit, Shotton started and finished a four-man move with a shot from 25 yards two minutes from time.