But even with Hyde's offensive explosion, the Buckeyes (10-0, 6-0 Big Ten) needed a third-quarter defensive stop and safety to recover the momentum.
After trailing 28-0 in the second quarter, Illinois (3-7, 0-6) closed to 35-21 in the third on two Nathan Scheelhaase touchdown passes.
Illinois had the momentum when the Buckeyes' Ryan Shazier sacked backup quarterback Reilly O'Toole in the end zone. Illinois recovered his fumble but the safety gave the Buckeyes a 37-21 edge and the ball. Minutes later, a Hyde touchdown put them up 44-21.
Hyde tacked on two late, long touchdowns runs of 55 and 51 yards.
Miller threw for 150 yards and two touchdowns.
Scheelhaase led the Illini with 288 yards passing and two touchdowns.
The Buckeyes defense kept Scheelhaase under pressure all day, sacking him five times and hitting him more than that.
It was one of those hits that kept Ohio State in control when Illinois was getting back into the game.
After Illinois closed to within two scores at 35-21, Scheelhaase had his helmet ripped off at his own goal line. Under the rules, he had to leave the game for a play, bringing O'Toole on.
The Buckeyes teed off on the backup quarterback, with Shazier hitting him from behind and knocking the ball loose. Tight end Matt LaCosse recovered the ball for Illinois to limit the damage to the safety.
The momentum swung swiftly back to the Buckeyes.
On the following drive, Ohio State moved quickly to the Illini 8-yard line.
Miller rolled left and threw an incomplete pass before taking a big hit from linebacker Jonathan Brown. The quarterback stayed on the turf for a time before briefly leaving the game.
Backup Kenny Guiton came on, handing off two plays later to Hyde for the 1-yard touchdown that put the game firmly back in the Buckeyes' grip at 44-21.
Miller's minute or so on the turf was a long one for the nervous Buckeyes, but he returned during the next series and finished the game.
Fast doesn't adequately describe how quick the Buckeyes came out Saturday.
Thirty-six seconds into the game, Miller ran up the middle of the Illinois defense for a 69-yard touchdown and a 7-0 lead. He slowed at about the Illinois 5-yard line, jogging the last couple of steps.
Over the next 15 minutes, it looked like it might be just that easy for a Buckeyes team in search of big wins that might convince voters that they belong in the national title picture.
Hyde put the Buckeyes up 14-0 with just under five minutes left in the opening quarter on an 18-yard touchdown pass from Miller.
Less than two minutes later, corner Bradley Roby added another touchdown, pulling down a tipped Scheelhaase pass and returning it 63 yards.
In those first 15 minutes, the Illini offense consisted of 88 yards and a pair of Scheelhaase interceptions.
But the Illini just wouldn't go away.
Down 28-0, V'Angelo Bentley returned a punt 67 yards for a touchdown with 7:29 left in the half to get the Illini on the board.
Then, down 35-7, Scheelhaase engineered two scoring drives that got Illinois back in the game.
The first ended with a 19-yard touchdown pass to Steve Hull with 2:25 left in the half to make the score 35-14. The second, early in the third quarter, ended with a 1-yard touchdown pass to Evan Wilson. The extra point pulled Illinois to within 35-21.