BOSTON — The Illinois men’s basketball team is so experienced that many of its players wouldn’t get carded at a local dive bar. They are physical enough that their frontline looks like they could be auditioning for linebacker spots at the NFL combine.

They balance that age and edge with an offense that can hum like a jazz band, with flourishes of deft passes and cuts that have formed one of country’s most efficient and effective units.

That harmony manifested itself in a first-half burst on Thursday night and a closing kick that allowed No. 3 Illinois to outlast No. 2 Iowa State 72-69 in the Round of 16 in the NCAA tournament on Saturday night.

Illinois solved the nation’s most efficient defense Saturday, jumping out with abandon in the opening minutes to build a 13-point lead and never relinquishing the lead to top Iowa State, which cut the lead to two three times in the final 10 minutes. Illinois scored the game’s first eight points and never flinched, enduring star Terrence Shannon Jr.’s second-half foul trouble and flummoxing Iowa State’s offense.

The spot in the Elite Eight continues Illinois’ deepest NCAA tournament run since 2005, when the Illini lost in the national title game. And the Illini teased with enough potential against the Cyclones that they left fans at the TD Garden wondering if they could prove a worthy foil to defending national champion UConn when they meet Saturday night with a spot in the Final Four on the line.

“We didn’t come here to win one game,” Illinois coach Brad Underwood said. “We came here to win two.”

UConn blasted No. 5 San Diego State 82-52 earlier Thursday to reaffirm the Huskies’ status as the country’s best team and the tournament’s No. 1 overall seed. UConn, which has lost just one game since late December, will face Illinois for the first time since 1994.

There were bursts in Thursday night’s game where Illinois looked like a worthy foil. Junior forward Luke Goode said the Illini will take a “why not us” mindset into the game as he said the veteran Illini “have seen it all.”

“I have more of a respect for them,” said Illinois forward Coleman Hawkins. “I think it’s a higher level of respect. I think they’ve been playing great all year. I think they’re well-coached, and they do what they do.”

The linchpin of any Illinois upset bid on Saturday will be Shannon, the star guard who finished with 29 points in Thursday’s win. That included sitting for more than five minutes in the second half after picking up his fourth foul with 11:17 remaining. He’s averaging 28.3 points per game in the NCAA tournament and has scored more than 25 in seven straight games.

Shannon hit a critical 3-pointer to boost the Illinois lead to five with nearly five minutes to go.

“He’s as aggressive an offensive player as there is in the country, and he is playing at such a high level,” Iowa State coach T.J. Otzelberger said. “You can’t let a guy like that get the opportunities that we allowed for him early where he got his confidence going.”

Illinois and Iowa State entered the game as the elite teams on opposite ends: Iowa State’s defense ranked No. 1 in adjusted defensive efficiency and Illinois brought the country’s No. 2 offense.

But it was Illinois’ defense — not a defining trait — that ended up sealing the game, as Shannon took a steal the length of the court and dunked the ball with 24 seconds remaining to give Illinois a six-point lead.

Iowa State played valiantly in the second half to come back, but their efforts were undone by some self-inflicted wounds, as they shot 13-for-28 on layups and dunks.

Illinois overcame its own hints at self-destruction, flopping at the free throw line. Coach Brad Underwood joked the Illini missed “102 free throws” — in reality they were 15-of-29.

All four of Illinois’ leading scorers are over 22 years old, and the collective roster is No. 11 in the country in KenPom.com’s experience metric. (Only Creighton is higher among teams left in the tournament.)

“We’ve played a lot of college basketball,” said Illinois guard Marcus Domask, a 23-year-old graduate student. “I’ve played a lot of teams that are supposed to beat us, if you say they’re supposed to beat us.”

Otzelberger pointed out that all of Illinois’ starters are 6-foot-6 or taller, giving them an imposing team that set a physical tone in the opening minutes against the Cyclones.

“They’re definitely an older, experienced, veteran group with some bigger bodies, and they were the more physical team for a large part of the game,” he said.

All that size and experience leave the Illini respectful of UConn, but undaunted.

“This is what you prepare for,” Goode said. “It’s super exciting to have the opportunity to go play the No. 1 team in the country in the Elite Eight. You can’t ask for anything better, honestly. It’s a blessing for all of us to have that opportunity.”