SPOKANE, Wash. -- For 36 minutes it looked like fifth-seeded Maryland was ready to make quick work of 12th-seeded South Dakota State.

And then, with their 18-point lead was trimmed to five with a little more than a minute left, sophomore point guard and leading scorer Melo Trimble fouled out. It made for a fast-and-furious finish, but Maryland's Jake Layman showed the same steady hand he had all game, hitting all four of his free throws in the final minute to propel Maryland to a 79-74 win in the first round of the NCAA Tournament on Friday.

Layman scored a season-high 27 points and Trimble had 15 of his 19 points in the first half and Maryland (26-8) looked ready to roll into a second-round meeting with Hawaii, an upset winner earlier in the day over fourth-seeded California.

"It's hard to win in this tournament, and I thought for 36 minutes we were really good," Maryland coach Mark Turgeon said. "Had an 11-point lead, and they hit back-to-back threes and everything changed. And that happens in this tournament."

Turgeon said he looked up at one point and was concerned with the Terrapins' inability to put South Dakota State away, even with a double-digit lead.

"If we were shooting the lights out and executing at a high level, it should have been a 20-point game. Instead, at the media timeout it was only 14, and I said, 'Dang, it seems like we should be up more than this.' But give them credit, they kept scoring during that stretch, too."

South Dakota State's George Marshall hit three free throws with 1:03 to play to pull the Jackrabbits within two points, but Layman drew a foul away from the ball with 43.1 seconds left and hit both free throws to push the lead to four.

Tevin King had a chance to cut the lead with two free throws with 24.4 seconds to play but could only hit one, South Dakota State's only miss from the line all night. Maryland then got the ball to Layman, who sank two more free throws to extend the Terrapins' lead to 76-71 with 18 seconds to go.

South Dakota State was not going away, however. After Maryland's Rasheed Sulaimon was whistled for a foul on Deondre Parks, who was awarded three free throws and hit them all to trim the Maryland advantage to 76-74 with 12.1 seconds to play.

When Maryland's Jaylen Brantley missed one of two free throws, the door was open for South Dakota State, but the Jackrabbits didn't call timeout and instead went right into their offense, turning the ball over in the backcourt.

The game ended on a Sulaimon breakaway dunk. If given the chance to do it again, South Dakota State coach Scott Nagy said he would have made a different call.

"I'm really proud of our kids that they didn't give up. If I had the final play over, I would have called a timeout," Nagy said. "We go through these things. We know what play we're running, we knew what to do, but we just had personnel in there that we don't normally have in there in those situations. And so, looking back on it, it would have been way better off for me to call a timeout and made sure we knew what to do."

Layman torched the Jackrabbits from deep all night, making 5 of 8 shots from 3-point range. He entered the game averaging 11.2 points, but seems to be heating up after scoring 26 in a win over Nebraska in the Big Ten tournament. Nagy said having Layman beat you is just one of the hazards of playing Maryland.

"Let's face it, here we are leaving a 6-9 tremendous shooter, great body, great athlete, we're having to leave him open because the posts are unbelievable, their point guard is unbelievable," Nagy said. "So, yeah, it is pick your poison. He's the one that probably won the game for them. He hit some big shots and made big plays for them.

Turgeon agreed and says he is seeing a different Layman of late.

"He's much more mature, he's playing with poise, he's playing with a great pace, he's guarded well all year, he's played tremendous defense, he's been a great leader," Turgeon said. "But the last four weeks he's gotten a lot more aggressive and he's just so confident in shooting the basketball. He was terrific today. We needed every point and every defensive play."

The Jackrabbits (26-8), champions of the Summit League, managed to keep the game tight early. A 3-pointer by Reed Tellinghuisen with 12:35 left in the first half pulled South Dakota State to a 10-10 tie. But then Trimble took over for a spell, scoring eight of the Terrapins' next 11 points to establish a cushion that would grow to a dozen by halftime.

South Dakota State freshman Mike Daum did what he could to keep the Jackrabbits in contention, scoring nine of his 16 points in the second half.

NOTES: This NCAA Tournament appearance was the third in five years for the Jackrabbits. ... Maryland freshman Diamond Stone had a quiet game, scoring four points and grabbing five rebounds in 22 minutes. ... George Marshall knows Big Ten opponents, having transferred to South Dakota State from Wisconsin. ... The teams were both efficient from the free-throw line, combing to hit 40 of 44, with Maryland hitting 24 of 27 and SDSU making 16 of 17. ... The teams combined for just four fast-break points all night and two of those came on Rasheed Sulaimon's game-ending dunk.