Randy Foye added 22 points, Kenneth Faried had 14 and J.J. Hickson had 11 points and 11 rebounds for the Nuggets. Brooks started in place of Ty Lawson, out due to a sinus infection. Wilson Chandler also sat out after receiving an injection to treat a hip injury.
Greg Monroe scored 22 points to lead the Pistons. Rodney Stuckey added 18 and Kyle Singler and Charlie Villanueva each had 13.
Trailing by seven at the half, the Nuggets rallied to take an 85-84 lead into the fourth quarter.
After Singler's 3-pointer put the Pistons in front 82-75, the Nuggets outscored Detroit 10-2 over the final 3:20 of the third quarter to regain the lead.
Brooks started the spurt with a 3-pointer and a driving reverse layup and Foye closed it by hitting a 3 and finishing a fast-break with a layup after stealing an inbounds pass.
Denver used another 10-2 surge to stretch its lead to 104-91 midway through the final period.
Detroit pulled to 113-109 with 54.2 seconds remaining as Singler and Villanueva hit 3s around a layup by Denver's J.J. Hickson. But Hickson had another layup and Anthony Randolph converted a three-point play to give the Nuggets a nine-point cushion with 31.7 seconds remaining.
Stuckey scored 14 of his points in the first half, helping the Pistons take a 61-54 lead.
Detroit led by as many as 11 points early on.
NOTES: Pistons C Andre Drummond sat the game out after injuring his neck on Saturday against Indiana. ... Pistons G Chauncey Billups, a former Nugget and native of Denver who has been sidelined by a knee injury, returned a warm ovation from the crowd with a couple of waves of his hand. ... The Pistons lost Josh Smith to ejection midway through the third quarter after he picked up a pair of technical fouls in quick succession. ... Brooks' previous career high for assists was 13 against Phoenix on Nov. 17, 2009.