The Daniels took the lead after just 7 minutes. Harry Vince slid the ball through to Tom Siddons who rounded Curtis Pond and netted from a tight angle.
Siddons doubled the hosts advantage in the 27th minute slotting low past Pond.
Chasetown had a lot of good possession in the final third. Danny Haystead pushed a shot away from the onrushing Liam Kirton before Ryan Wynter headed into the side netting.
A minute before half time, Will Whieldon tested the keeper with a free kick that Haystead superbly pushed wide for a corner.
Stamford had two early penalty appeals turned down at the start of the second half as they attempted to extend their lead.
Kirton flashed an effort just wide from a Chasetown corner midway through the second period.
Neither side created much in the second period in a game that rarely got going after the break.