An all-American center at his best, a coach happy to be here so his crippled mother could see him work, and a ton of free throws carried Purdue to a 68-60 victory in today's NCAA Mideast Regional championship game over a Duke basketball team so frustrated one of its players angrily swung a towel at a referee.

In a matchup that figured to be critical, Joe Barry Carroll, Purdue's 7-foot-1 all-American, outscored Duke's Mike Gminski, 26-17, and sank four important free throws in the last minute. So the Boilermakers advance into the national tournament semifinals next weekend against the most unlikely of Cinderella teams, UCLA.

The Purdue coach, Lee Rose, grew up two miles from Rupp Arena and counts among his fondest memories the days he sold soft drinks during games played by Adolph Rupp's Kentucky teams. Rose did himself proud today in that arena with a piece of brainwork, that (a) gave Carroll three minutes rest, (b) put Duke into a panic attack, and (c) produced 17 successful free throws in the last 8 1/2 minutes.

And when Duke had failed in its frantic scratching at the Purdue lead in those dwindling last minutes of a season memorable for good times and bad, its junior forward Kenny Dennard moved toward a referee and swung a towel at him. Two Kentucky state troopers stepped between the men.

"Is that true?" Dennard said when asked of the incident, adding, "No big deal." The referee, Bob Herrold, refused comment.

Ahead by as many as seven points in the first half, Duke led through 4 1/2 minutes of the second half and didn't fall behind for good until the last 10 minutes. Then Purdue, third-place finisher in the Big Ten this season, was hanging on to a three-point lead when Rose made the coaching move that may have earned his team its 22nd victory in 31 tries.

After Dennard's tip-in made it 51-48 with 8:05 to play, Rose told his charges to sit on the ball until it went flat. The coach who took North Carolina-Charlotte to the final four in 1977 had Carroll resting on the bench. He saw that Duke had Gminski and Gene Banks at the scorer's table, itching to go in.

Sit on it, the Boilermakers did. For 3:11, they played the sort of keepaway so often seen in the Atlantic Coast Conference, where Duke finished fifth before winning the postseason tournament and two NCAA games to come here today with a shiny 24-8 record and the favorite's role over a team 20th in one poll and out of sight in the other.

For 3:11 Purdue rested Carroll who would score seven more points (to Gminski's four) when he played the last 4:54 and helped make Duke the fifth of five ACC entries to leave the NCAA chase.

"I saw Gminski and Banks waiting, yes, and that's why we didn't shoot in those three minutes," Rose said. "We got three minutes that were very precious."

Duke finally fouled Drake Morris to end the waiting game and the Purdue forward made two free throws to raise his team's lead to 53-48.

After a Banks layup, Purdue scored the next five points, all on free throws, four more by Morris, and the Boilermakers took an eight-point lead at 58-50 with 3:09 left.

Had Duke been working with the wonderful efficiency that carried it to successive victories over the three top-seeded teams in the ACC tournament two weeks ago, the Blue Devils might have had a chance today even so far behind with so little time to play.

But today Duke was not a good team.It had 22 turnovers to Purdue's 17. It committed 25 fouls to Purdue's 17. 'it had 28 rebounds, Purdue 33. Down the stretch in those critical last three minutes, Duke "didn't make the key shots," as Coach Bill Foster said, and repeatedly failed to take advantage of chances provided by the Boilermakers, who were none too elegant themselves.

The closest Duke came was at 58-54 on a 20 footer by Bob Bender and a short jumper by Banks. There were 2 1/2 minutes to play.

Only 38 seconds later, though, it was over. Carroll, a very quick big man with a nice shooting touch, rolled in a layup. Fouled by Banks, the big guy averaging 22 points a game added the free throw and Purdue's lead was back to eight at 62-54.

This was not a pretty game. This was a, how you say, a very, very ugly game. Both teams shot 44.2 percent. On the run with a fast break once, Duke was three-on-nobody and passed the ball out of bounds. Gminski jammed a shot into the underside of the backboard. A notoriously poor shooting team from outside, Purdue was read out at halftime by Rose for "shooting from the first aisle of the bleaches."

Basketball in the bluegrass is not canceled for lack of pulchritude, however, and the astounding crowd here -- 22,800 two days after Kentucky was eliminated -- probably believed Rose when he said he didn't much mind the frenzied frolicking because, after all, his guys were trying hard.

"Trying too hard, really," said Rose, who joins a tiny circle of coaches to take two different schools to the final four.

"Our biggest problem was not on defense," said Foster, the lame-duck coach who will take a six-year Duke record of 113-64 to South Carolina. "It was offensive . . . . When we had a problem with 11 minutes to go in the first half (once leading, 18-11, Duke made only two baskets in five minutes), we made four turnovers in five trips down the floor."

He was asked if it were special for a hometown boy to win a championship here, and Rose said, "This will sound corny, but yes, because my mother gets to see it. She's crippled, she's 73 years old. We lived right next door to Memorial Coliseum and I used to play in the rafters and I sold Coca-Colas at the games.And the first time I brought my Charlotte team into Rupp Arena, Coach Rupp hugged me."

One thing more. Purdue's players raised Rose up to cut the last strand of the net taken in celebration. It's unusual, someone said, for players to lift a coach up to the rim.

"If they didn't lift me, said the happy kid from the rafters of old, "they don't go to Indianapolis."