KANSAS CITY, Mo. -- Moments after a scare against Southern Illinois, Missouri coach Quin Snyder was shrugging, firm that the Tigers never underestimated the underdog Salukis.

"A lot of people didn't think we were going to win this game," he said after Missouri, on Ricky Paulding's free throw with 4.1 seconds left, eked out a 72-71 victory Thursday in a Midwest Regional opener.

It's a safe bet the sixth-seeded Tigers (22-10) aren't overlooking who's next in their NCAA tournament regional at Indianapolis: a Marquette team that weathered its own little hair-raiser.

The third-seeded Golden Eagles (24-5) -- Conference-USA's regular-season champions -- withstood 14th-seeded Holy Cross 72-68 for their first first-round victory in seven years.

Now, the two teams that managed to march on after two great escapes tangle today, each intent on sending the other packing in what many expect to be another grinder.

The winner advances to the Sweet 16 for a regional semifinal next Thursday at Minneapolis.

In advance of today's showdown, Missouri and Marquette each looked to play better than their opening-round close shaves.

Among Marquette's challenges: Defend the perimeter, where Missouri -- largely their gifted young guards -- has launched an average of 20 3-point attempts per game, with 36 percent efficiency. And find a way to stifle Arthur Johnson, the Tigers' hulking, 260-pound inside force who entered the tournament averaging more than 15 points and nine rebounds.

Missouri's test: disrupt Marquette's playmaker Dwyane Wade -- Conference-USA's player of the year -- and his steady sidekick, Travis Diener, the Golden Eagles' star against Holy Cross.

"We've been through a lot of adversity," Paulding said after Missouri moved on Thursday despite its season-high 23 turnovers. "Things seem to not be going our way, and we just show that we're a tough team."

A little proof: Missouri has trailed in the second half of its past four games but still found ways to win three of them.

"No, we don't feel lucky at all. We fought for 40 minutes," Johnson said after his 24 points and 11 rebounds -- one short of his season-high -- against upset-minded Southern Illinois.

"Once they got the ball in to Johnson, there wasn't much we could do," Southern Illinois coach Bruce Weber lamented. "Arthur Johnson is a load. He's a monster."

Johnson and fellow big man Travon Bryant combined for 41 points, 20 rebounds and five blocked shots, helping Missouri overcome poor guard play by Jimmy McKinney and Ricky Clemons.

So on comes Marquette, a team known more for its backcourt of Wade and Diener. Both came up huge Thursday in extending Marquette's season: Wade had 15 points -- all in the second half -- to Diener's career-high 29 points on 6-for-7 shooting from 3-point range.

"I got a few looks and I took them," Diener said. "It's not like I was looking to take bad shots. They just came."

That's something Missouri hopes to fearlessly frustrate.

"If you end up playing with fear, that's the game that you really lose, and you end up losing a bigger one after that," Bryant said. "You can't have fear. There's only one team that's going to be eventual national champion. We want it to be ourselves."