Miller broke up a tight game at Red Bull Arena when he streaked across the goalmouth and headed Russell Teibert's looping cross from the right side of the penalty area for his third goal of the season.
Motherwell had another chance to draw level five minutes into the second half, Hammell's cross finding its way to Ian Russell, but his shot was well off target.
Four members of the Parachute Regiment - Pte Paul Coleman, Maj Adam Dawson, Maj Russell Lewis and Maj John McDonald - were awarded the Military Cross for their service in Afghanistan.
Beresford still had to thwart substitutes Ian Henderson and Darel Russell in quick succession before Little made the game safe by squeezing home another Blake cross.