Al Jefferson tallied 13 points and 10 rebounds for Charlotte, which has dropped three straight contests.
The Pistons scored the final eight points of the first half to break a tie and caused further separation during the late stages of the third quarter.
After Gerald Henderson knotted the contest at 46-46 late in the second with a jumper, Detroit capped its 8-0 swing when Augustin knocked down a 3-pointer and Monroe hit a short jumper for a 54-46 advantage heading into the locker room.
Kyle Singler poured in six points during a 16-4 Pistons surge to close the third, with Monroe's layup at the horn staking them to an 83-60 margin going into the fourth.
Detroit, which trailed 27-26 following a quarter of play, cruised to the easy win over the final 12 minutes.
Drummond was a rebound shy of his sixth straight double-double ... Detroit improved to 4-8 since point guard Brandon Jennings went down with a torn Achilles ... Detroit held a 50-32 points in the paint advantage ... Henderson netted 17 points for Charlotte.