The top-seeded Pistons - trailing 3-2 in the best-of-seven series before Friday's must-win game in Cleveland - produced a dazzling early onslaught to build a double-digit lead that proved the difference between the two sides.
Cleveland, unbeaten at their Rocket Arena home so far this postseason, will now have to win on the road in Sunday's decisive game seven in Detroit to advance.
Cunningham's 21 points included five three-pointers, while at the defensive end, Detroit center Jalen Duren delivered a dominant performance that included 11 rebounds, three blocks, and a steal.
Cunningham was one of six Pistons players to finish in double figures, with Paul Reed adding 17 off the bench, and Duren and Daniss Jenkins scoring 15 points apiece.
"We're just playing our brand of basketball, coming out competing, trying to execute our system to the best of our ability, and we're together," Cunningham said afterward.
"We stick together through everything, so it's a great win for us."
James Harden led Cleveland's scoring with 23 points while Donovan Mitchell was restricted to 18 points.
The Cavs started Friday's game brightly, opening up a six-point lead in the first quarter before the Pistons started firing to take a grip on the contest.
A devastating 22-4 run by Detroit saw the visitors accelerate into a commanding 39-27 lead in the second quarter, and although Cleveland closed the gap to 54-51 at halftime, the Pistons regrouped impressively to snuff out the Cavs' threat with a 30-19 third quarter.
That left Detroit leading by 14 points heading into the fourth, and the result was never in doubt, with the Pistons maintaining a double-digit lead to close out victory.