Monroe had 16 points, 11 rebounds and five assists on 6-of-11 shooting from the field in just over 31 minutes. Drummond came off the bench to record 13 points, 10 rebounds and two blocks on 5-of-7 shooting from the field in just under 19 minutes.
Monroe ranked ninth in the league last year with 30 double-doubles. Drummond, the ninth overall selection in the 2012 NBA Draft, had 10 double-doubles in college last season for the Connecticut Huskies.
Pistons rookie Kim English recorded two points and three rebounds with a steal and a block in just over 15 minutes of playing time.
The Hawks were led by Lou Williams who had 12 points off the bench.
With the win, the Pistons improved to 4-4 in the preseason. Detroit opens the regular season against the Houston Rockets on Oct. 31.