Giannis Antetokounmpo scored a play-off career-high 41 points as his side progressed to the Eastern Conference semi-finals for the first time since 2001.
Detroit looked to be in charge early on, holding a six-point lead by half-time, but the third quarter proved the turning point, with Antetokounmpo scoring 16 points to help erase the Pistons' advantage.
The Bucks went on to build a 15-point lead in the fourth and were left in no danger of progressing to the second round, where they will face the Boston Celtics.
Donovan Mitchell finished with 31 points after racking up 19 points in a fourth-quarter rally – the Jazz outscoring their opponents 31-12 in the final 12 minutes.
James Harden top-scored for Houston with 30 points but it was not enough to eliminate the Jazz, who now head to Houston for game five, trailing the series 3-1.