He was hired last November to revive the beleaguered Buckeyes.
The slow-starting Miller, who stutter-stepped for a 65-yard score just 17 seconds into the second half, was 14-of-24 passing for 207 yards. He connected with Devin Smith for a highlight-reel score and also hit Corey Brown on a 5-yard TD pass.
After Miller's long run made it 28-3, Bradley Roby recovered a high Miami punt snap in the end zone, and the rout was on.
Travis Howard had two interceptions, and Carlos Hyde scored on 4- and 8-yard runs for Ohio State.
Miller and Hyde, who had 82 yards on 17 carries, helped the Buckeyes roll up 294 yards on the ground and 244 through the air.
Much like during the early spring, when Meyer called the attempts to learn his new hurry-up, spread offense a "clown show," the Buckeyes struggled at the outset. With Miller completing just one of his first seven passes, Ohio State was outgained 172 to 48 in the opening quarter before a stunned crowd of 105,039 at Ohio Stadium that came expecting to see a refurbished and cutting-edge offense. The first four possessions ended with punts.
Meanwhile, the RedHawks bumbled despite taking a 3-0 lead after the first 15 minutes.
Zac Dysert, who completed 31 of 53 passes for 303 yards and one touchdown with the two interceptions, was victimized by dropped catches again and again. Three times it appeared the RedHawks had a first down after a catch when the ball abruptly came loose.
Smith's spectacular reception turned the tide.
The Buckeyes, who took over at their own 17 after a punt, needed just four plays to cover the distance and take the lead for good. Miller used a play-action fake to freeze the defense before hitting Brown for a 38-yard gain to the Miami 23. Miller then threw high and hard into the right corner of the end zone, where Smith leaped, snagged the ball with his right hand and, while twisting, tucked it in as he crashed to the ground.
The Buckeyes kept it up once they figured out how to score.
Miller rolled right and flipped a short pass to Brown for a TD before Hyde burst in off right tackle for a 21-3 lead.
A 44-yard throw from Miller to Evan Spencer with 3 seconds left in the half gave Ohio State the ball at the 1, but Hyde was stopped by Miami's Justin Bowers short of the goal line.
Miller scored just 17 seconds into the second half by juking then speeding past the Redhawks' D.J. Brown down the left sideline for the lengthy score.
Meyer took over a battered program that was nailed by suspensions and NCAA investigations while going 6-7 last year, the program's first losing record since 1988. The Buckeyes are banned from playing in a bowl game after the season as a result of NCAA violations committed under the Jim Tressel regime.