Theo Pinson of the North Carolina Tar Heels shoots in the second half of Saturday night’s Final Four game against Oregon. (Photo by Tom Pennington/Getty Images) (Tom Pennington/Getty Images)

Some 362 wincing, striving days after a rapid-eye-movement nightmare flooded their brains and seeded their determination, North Carolina clung onto the last rung of a 10-point lead Saturday night and began clanging free throws. A dreary, formless national semifinal with Oregon had wound its way into something oddly stirring. A bloated University of Phoenix Stadium crowd of 77,612 had finally taken to gasping.

When the Tar Heels finally did wind up exhaling and exulting, they had added to the array of inconveniences they had collected and surmounted in their bid to return to the final Monday night of the season and carve out some less haunting memories. Their 77-76 win over a band of Ducks that couldn’t shoot well but kept trying will be remembered for its clunky closing sequence.

“Oh, jump off a building, something like that,” Coach Roy Williams joked of that sequence.

When all the two teams’ 77 missed shots (out of 126) and the 32 missed three-point shots (out of 47), and all the bounty of rebounds (43 for each side) had subsided to the last six seconds, the Tar Heels (32-7) would go to the free throw line twice with that 77-76 lead.

Kennedy Meeks, their immense big man who had an immense game, missed two with 5.8 seconds left.

Joel Berry II, their floor leader with the 2-for-14 game, missed two more with four seconds left.

On both occasions, something weird happened. Jordan Bell, the Oregon monster in the middle who had rebounded and enforced his way through this NCAA tournament, wound up sobbing heavily in the corner after missing two rebounds in a game in which he had 16. “I lost this game for us,” he said sadly later. On the first, North Carolina’s 6-foot-6 Theo Pinson soared to bat the ball out and necessitate another foul. On the second, Meeks outfoxed two opponents with scant contact and took that thing and North Carolina’s season-long mission in his considerable hands.

“Nobody wins a game like that,” Pinson said. “Well, I guess we did. But it was definitely the weirdest game.”

Largely on the force of Meeks’s 25 points and 14 rebounds, the Tar Heels will become the first team since Butler in 2011, and only the third in the 2000s, to turn up in uniform for two straight closing Monday nights when they oppose Gonzaga. More evocatively, they will return to the stage of their Villanova nightmare, even if it will be a desert football stadium rather than a Texas football stadium, and even if it will happen against a private Pacific Northwest university of 7,572 students rather than a private Philadelphia university of 10,000.

It will happen because they mirrored their knack from two other hard games of March: They surmounted, or held off, inconveniences. They trailed Arkansas by five points with 3:31 left in the second round, Kentucky by five points with five minutes left in the South Region final and Oregon by eight points in the first half of the national semifinal.

They insisted on pushing and demonstrated how, when pushing, it’s best to have somebody 6 feet 10 and 260 pounds doing the pushing. Meeks, who played 21 unremembered minutes on the final Monday night of 2015-16, splurged during the final Saturday night of 2016-17. After he missed his first shot on an odd, clunky jumper from the lane, he strung together enough layups, dunks and putbacks for the runaway efficiency of 11 straight field goals. He wound up on a shiny 11 for 13, and he spiced the work with 14 rebounds, only three fewer than the bonanza to which he had treated Kentucky.

Along his way, he saw 6-8 teammate Justin Jackson use his acrobatic floating arts and other skills to nearly catch up, so that by the end they had 47 points between them, a 32-7 record and Monday night plans. They left the kind of regret they carried into last off-season in the possession of Oregon, which reached its program’s first Final Four since 1939 and hammered at that 10-point deficit even though it spent the second half shooting 3 for 18 from three-point range.

“Neither of us shot it very well,” Oregon Coach Dana Altman said, “but obviously there weren’t a lot of wide-open shots to be had.”

Of the nine North Carolina players who saw minutes in the famous 77-74 loss to Villanova, six remain at the school in its record 20th Final Four. All six got Williams’s call Saturday night, especially Meeks and Jackson. Back in Houston, Meeks had played 21 minutes with four points and seven rebounds on 1-for-8 shooting, while Jackson played 34 minutes with nine points and four rebounds on 3-for-8 shooting. Both aimed all offseason and all winter to soothe both those and other memories, particularly the one all set for galling replay for the rest of their lives, that of Kris Jenkins’s storybook three-point winner for Villanova.

In that mission, they had more nuisance against the 33-6 Pacific-12 Conference champion. Their wish to coax foul trouble from Bell wasn’t granted as Bell helped himself to 13 points and 16 rebounds. Berry’s bleak shots and four of five late missed free throws often left things messy. When Oregon’s Dylan Ennis rained in two three-point shots from the corner in the 16th minute of the first half, Oregon led 30-22. North Carolina used mostly its inside force to eradicate that, then used an epitome of grinding — two, last, desperate offensive rebounds — to quell the last gasps.