Draper had arrived in Florida on the back of a quarter-final run at Indian Wells, just his second ATP Tour event after an extended spell out with an arm injury, but was unable to build on that momentum.
Opelka produced a dominant serving display to beat 25th seed Draper 7-6(3) 7-6(0), firing 25 aces and 47 winners to reach the third round on home soil.
"I didn't have many chances, especially on his serve," Draper told reporters. "I didn't get broken in the match so that was kind of my job, right?"
Earlier, after rain disrupted play in Miami Gardens, fellow American Quinn saved seven set points on his way to a 6-4 7-6(7) victory over Ruud, progressing for the first time in his career to a third round at a Masters 1000 event.
Italy's Matteo Berrettini, a former world number six, also clinched a surprise 6-4 6-4 win over 10th seed Alexander Bublik.
Top seeds advance
Persistent rain forced further scheduling changes, with several matches pushed to Saturday, while world number one and newly crowned Indian Wells champion Aryna Sabalenka was moved to a secondary court to face Ann Li.
Sabalenka survived a stern battle against her American opponent, grinding out a 7-6(5) 6-4 victory to reach the third round.
"I was there, I was fighting no matter what, even though my game probably wasn't the best one that I have," Sabalenka said in her on-court interview.
"She played incredible tennis - she was super aggressive and she served incredibly."
Men's top seed Carlos Alcaraz later kept his title charge on track, sailing through to the next round with a composed 6-4 6-4 win over Brazilian teenager Joao Fonseca.
World number two Elena Rybakina continued her tremendous form, defeating her Kazakh compatriot Yulia Putintseva 6-3 6-3.