Pachulia also thrived with extended playing time, scoring all 11 of his points in the second quarter as the Hawks took a 55-51 halftime lead.
The Hawks' biggest lead was 73-62 at the end of a 10-0 run in the third period.
Gallinari had 16 points and JaVale McGee had 11 for Denver. Iguodala shot only 2 of 10 for five points, including the late 3-pointer, and a game-high seven turnovers.
Devin Harris had 12 points for Atlanta. Williams led the Hawks with six assists.
NOTES: The Hawks ended a four-game losing streak in the series with their first win over the Nuggets since Nov. 7, 2009. ... Hawks G Kyle Korver was away from the team and with his wife, who is expecting the couple's first child. The team recalled rookie G John Jenkins from its Bakersfield NBA Development League affiliate. Jenkins did not play. ... Lawson and Andre Miller each had seven assists.