GLENDALE, Ariz. — The College Football Playoff has delivered so many duds that it makes you forget it can deliver something like this.

The first of two semifinals on Saturday was a staggering, stupendous show that looked as if it were over at halftime, then looked finished in the third quarter and once more in the fourth, but never quite was — until the end. Again and again, Michigan fought back. And again and again, TCU kept the Wolverines at arm’s length.

At the end, purple confetti rained down on State Farm Stadium after TCU scored a monumental 51-45 upset over Michigan in an utterly mad, wildly brilliant Fiesta Bowl. The Horned Frogs (13-1) will play a week from Monday for a chance at their third national championship, and their first since an 11-0 season in 1938.

The Horned Frogs dominated the first half, going up 21-6, but victory did not come easily. Starting in the third quarter, the game turned into a roaring festival of points, with TCU successfully holding at bay comeback attempt after comeback attempt by Michigan via its own offensive prowess and the brilliance of quarterback Max Duggan. All hell broke loose, over and over.

Michigan (13-1) pulled within 41-38 two plays into the fourth quarter after Emari Demercado’s fumble set up a Roman Wilson score and a Ronnie Bell two-point conversion. The Horned Frogs punched right back, though, with Quinton Johnson taking a crossing route 76 yards to the house to extend the lead to 10.

The Horned Frogs’ lead got back to 13, after another TCU field goal, before Michigan mounted its last scrambling attempt at a comeback. J.J. McCarthy led the Wolverines on a nine-play, 56-yard drive, ending in a Wilson touchdown, to bring the score to 51-45.

TCU got the ball back needing to kill the clock, and ended up doing so successfully, with Duggan converting on third-and-one at the Horned Frogs’ 20-yard line to force the Wolverines to use up their three timeouts before they got the ball back with 52 seconds to go at their own 25.

McCarthy, so brilliant in getting Michigan back with a chance, fell short, as the Wolverines failed to pick up a first down.

A pair of McCarthy throws to Bell brought Michigan back into the game at the start of the third quarter. First, McCarthy found Bell on a corner route for 43 yards, setting up a field goal to cut TCU’s lead to 21-9. Then, following a Mike Sainristil interception, McCarthy hit Bell on a flea-flicker for a 34-yard touchdown. Suddenly, after looking dead in the water in the first half, Michigan was within one score before the six-minute mark of the third quarter. It was game on.

From there, TCU scored 20 more points in the third quarter and Michigan scored nine, fighting back multiple times when the game looked over. Finally, as the page was about to turn to the fourth quarter, Michigan recovered a TCU fumble to set up a chance to get within a score — and everyone in the vicinity took the chance to breathe.

Fifteen minutes of game clock later, it was the Horned Frogs breathing a little lighter, their mettle confirmed.

Michigan came in as a heavy favorite, the conventional wisdom being that the better-tested Wolverines could use their physical run game to push around TCU. Despite that perceived physical edge, it was Michigan that was pushed around all game long.

TCU looked more prepared, better-coached and more ready for the moment. And Michigan had little answer for the Horned Frogs’ physicality.

In one year of coaching TCU, Sonny Dykes might already have elevated himself to program lore alongside Gary Patterson, who spent 20 years building the Horned Frogs up before he was fired in the middle of last season. At the time, it looked like the program was going stale. The Horned Frogs finished last season 5-7 and missed a bowl for the third straight year.

Even this season, as they started to rack up wins, it was easy to overlook a team that seemed to rely on comebacks and scored few emphatic victories against a weak Big 12 conference.

No one, though, will look past TCU anymore.