So it was for coach Bruce Pearl’s sixth-seeded University of Tennessee Volunteers in yesterday’s second-round Midwest Regional game at Dunkin’ Donuts Center.

Oh, the Vols had all the credentials to think they were worthy of a Sweet 16 berth next week in St. Louis. They had won 26 games and done it in the Southeastern Conference, which is never a day at the beach, even in off years. They had done some giant toppling of their own, with wins over this year’s blue bloods, Kansas and Kentucky.

And they had survived a grinder game by knocking off No. 11 seed San Diego State Thursday night. But now they had to deal with a real underdog — No. 14 seed Ohio.

The Bobcats had snuck into the Mid-American Conference tournament as the No. 9 seed, with 14 losses. Then they started winning. They earned an NCAA bid by beating Akron in overtime. And on Thursday night, they stunned the college basketball world with a 97-83 victory over Georgetown.

Could coach John Groce’s Bobcats do it again? The tone had been set earlier when 10th-seeded Saint Mary’s upset No. 2 seed Villanova in a South Regional game.

The answer — thankfully, for the Vols — was no. The Volunteers took care of business with an 83-68 victory that put them into Thursday’s regional semifinals against the winner of today’s game between Ohio State and Georgia Tech.

As is the case in most of the Vols’ games, this one wasn’t pretty. The teams combined for 30 turnovers, there were 17 steals, and most important from the standpoint of the Volunteers, it was a defense-oriented game dominated by a Tennessee team that is taller and more talented than Ohio.

“We knew going into the game that protecting the paint was going to be very important,’’ said Groce. “And they outscored us, 58-12, on paint points.’’

Pearl, who was worried about the Bobcats’ guards — particularly Armon Bassett, who had shredded Georgetown for 32 points — told his team to be more aggressive on defense, put pressure on Ohio from the start.

And in a game in which the Vols raced to a 38-27 lead, and allowed the Bobcats (22-15) to sneak back to within worrying range (5 points) a few times in the second half before coasting into the Sweet 16 for the fifth time, Bassett had a miserable day, with just 7 points and on 2-of-10 shooting.

“There were some numbers that stand out,’’ said Pearl. “Particularly defensively. When Ohio outshoots their opponents, they win at a high percentage. When they score 70 or less, their chances of winning go way down.’’

One of the reasons why neither Bassett nor freshman D.J. Cooper — who had scored 23 points against Georgetown and was limited to 16 by the Vols — performed under par was the harassment of Bobby Maze, who scored only 3 points, but had 4 rebounds, 9 assists, and 2 steals. “I think our defense created a lot of our offense,’’ said Maze. “We got steals, deflections, and made plays.’’

Tennessee (27-8) now moves to the Sweet 16, where it’s been four times in the last five years. The problem has been reaching the Elite Eight. The Vols are 0-5 in the Round of 16.

Of the teams remaining in the tournament, Tennessee can still be classified as a Goliath. The wins over Kansas and Kentucky guarantee that status, and there is no question the Vols’ talent is elite. Getting that talent to perform on a consistent basis away from Knoxville has been one of Pearl’s biggest challenges.

“One more [win] would get us to someplace we’ve not been before, and that’s the Elite Eight,’’ said Pearl. “So certainly the team has got great motivation to accomplish that.’’

The two wins signify little, since both San Diego State and Ohio were decided underdogs. The bar figures to be raised considerably in St. Louis.

Whether the Volunteers can clear that bar is the question.

Mark Blaudschun can be reached at blaudschun@globe.com.