Eastern Conference leaders Detroit looked to be cruising towards a comfortable win after surging into a 20-point lead early in the third quarter after a 37-point second period.
But Denver star Nikola Jokic rallied with 10 points in the third quarter and Jamal Murray poured in 14 points in the fourth to reduce the Pistons' lead to single digits in the final minutes.
Cunningham, though, was equal to the challenge, draining two crucial late free throws to give Detroit a five-point lead with nine seconds remaining as the Pistons closed out the win.
Jamal Murray led Denver's scoring with 32 points while Jokic finished with 24 points, 15 rebounds, and four assists.
All five Detroit starters finished in double figures, with Cunningham supported by 20 points from Duncan Robinson – including six three-pointers – and Jalen Duren 19 points.
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The win gives Detroit a 37-12 record at the top of the Eastern Conference, five-and-a-half games clear of the second-placed New York Knicks, who extended their winning streak to seven games with a 132-101 blowout over the Washington Wizards on Tuesday.
Mikal Bridges scored 23 points and Jalen Brunson added 21 in a wire-to-wire romp for the Knicks, who led by as many as 41 points in the fourth quarter. The Knicks are 32-18.
The Boston Celtics remain third in the standings and are also on 32-18 after a 110-100 defeat of the Dallas Mavericks in Texas.
Mavs rookie sensation Cooper Flagg once again lit up the American Airlines Center with a dazzling 36-point display, but Dallas were always struggling to get close to a Celtics team who led from the end of the first quarter.
Jaylen Brown's 33 points led the Celtics scoring, with Payton Pritchard adding 26 off the bench.
In the Western Conference, the reigning NBA champion Oklahoma City Thunder became the first team this season to record 40 wins with a 128-92 demolition of the Orlando Magic.
Oklahoma City accelerated into a 25-point lead at the end of the first quarter and coasted home with ease as reigning MVP Shai Gilgeous-Alexander continued his incredible 20-point scoring streak.
The Canadian star, who finished with 20 points, nine assists, and five rebounds, has now scored 20 points or more in 121 consecutive games and is just six games away from breaking Wilt Chamberlain's longstanding record of 126 set between 1961 and 1963.
Elsewhere, the Los Angeles Lakers wrapped up their road trip with a 125-109 rout of the Brooklyn Nets.
LeBron James impressed with 25 points, and Luka Doncic scored 24, while the Lakers also welcomed back Austin Reaves from injury after a month-long layoff. Reaves finished with 15 points off the bench.