The 49ers, who lost players to injury, illness and international paperwork problems this season, overcame the Rams and their sophomore sensation 81-70 in overtime in the first round of the NCAA Midwest Regional.
"They just did a great job on defense," said Odom, who finished with 16 points and 12 rebounds. "They did a great job on me today."
Marlon Thomas scored five of his 13 points in overtime and helped stymie Odom as the fifth-seeded 49ers advanced to the second round.
The 12th-seeded but slightly favored Rams (20-13), who won the Atlantic 10 postseason crown on Odom's buzzer-beating 3-pointer, blew an eight-point first-half lead and were outscored 16-5 in the extra period.
In regulation, Jobey Thomas' 3-pointer with 37 seconds left put North Carolina-Charlotte ahead 65-63, but Antonio Reynolds-Dean tied it with 16 seconds remaining.
Jobey Thomas's closely contested baseline jumper wasn't close at the buzzer. But it was all 49ers in overtime.
Marlon Thomas's putback and 3-pointer put the 49ers on top 70-66 with three minutes left, and Kelvin Price's basket at 1:23 made it 72-66.
The 49ers then hit 9 of 11 free throws to ice it.
Galen Young, Charlotte's leading scorer, had 17 points before fouling out with 3:59 left in regulation.
"I told him he'd be more rested now," joked 49ers coach Bobby Lutz.
Price added 15 points and 11 rebounds for UNC-Charlotte.
Odom, who sat out last season after transferring from UNLV and who could be the top pick in this summer's NBA draft, was stymied by Young and the 49ers' dizzying display of defensive switches.
Odom picked up three fouls in the first half.
"I know he prefers to go left," Young said. "He'll always spin back to his strong hand. He ducked his shoulder a few times, and I decided to just take the charge rather than try to fight him."
Young wasn't alone in frustrating Odom.
"Marlon Thomas had a tremendous game off the bench," 49ers coach Bobby Lutz said. "He did a marvelous job on Lamar Odom in overtime after Galen fouled out."
"I think he got a little frustrated because out on the court, he was calling for the ball," Marlon Thomas said. "Galen's a real physical player. I'm not as physical, so I just tried to be smarter than Lamar Odom."
The 49ers trailed 36-31 at halftime but overcoming obstacles has become old hat for them.
They lost star center DeMarco Johnson to the NBA and coach Melvin Watkins to Texas A&M in the offseason. Then, redshirt freshman Ouseynou Kane got stuck in Senegal because of visa problems and guard Dalonte Hill was lost for the season with a knee injury in September. Finally, redshirt freshman Charles Haywad's leukemia returned in December.
Rhode Island had to replace three starters, including both guards, from the team that reached the final eight last season, but coach Jim Harrick's squad was still a 1 1/2 -point favorite Friday, mostly because of Odom, who wouldn't say that he's going pro.
"That's going to be way down the road," he said. "I have a long time to decide that."
After the game, Lutz hollered in the direction of Harrick, who shouted back.
"He just came out of the box and came way down the lane and yelled something to me," Harrick said. "In 35 years, I've never had another coach yell at me and I didn't appreciate it."
"Just the heat of the moment," said Lutz, who later issued a statement contending he was screaming at an official and not Harrick.
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