Davis, a 6-foot-9, 310-pound sophomore nicknamed "Big Baby," took over after missing eight of his first nine shots and being held to five points in the opening half. He finished 7-of-15 from the field and had 13 rebounds, and left Iona's Ricky Soliver shaking his head in amazement.
"I didn't know he was that big," Soliver said. "When we were warming up, I saw him and my eyes just opened up. He's a load down there. I didn't think he was that much of a problem. But a big guy like that shooting fadeaways? He killed us down low."
Soliver and Steve Burtt, the highest-scoring guard tandem in Division I, did all they could to keep Iona (23-8) in the game. Burtt had 23 points and Soliver 14 in their final college contests, but were a combined 2-for-14 on 3-point attempts.
LSU (24-8), which trailed 37-32 at the half, rebounded from a disappointing loss to Florida in the SEC tournament to advance to a second-round matchup against either fifth-seeded Syracuse or No. 12 Texas A&M on Saturday.
Darrel Mitchell scored 19 for the Tigers, who used an 18-7 run to pull away from a 38-38 tie. Iona trimmed an 11-point deficit to 60-57 with about six minutes left, but LSU spurted again with Davis delivering a fallaway jumper in the lane to key a 10-0 run.
LSU shot 65 percent in the second half, with Davis making six of seven shots to wear down Iona's exhausted frontcourt.
"I was analyzing the guys' nonverbal communication. I learned that in sociology," Davis said. "When I see that, when I see fatigue, some negative things, you've got to go straight at them."
After falling short in the SEC tournament the last two seasons and playing poorly in a first-round loss to UAB in last year's NCAAs, LSU feels it needs to make a strong run to essentially validate the progress coach John Brady has made in rebuilding the Tigers' program.
Davis has been a big part of the success and figured to give LSU a significant advantage against a guard-oriented team like Iona, whose tallest defenders all yielded at least 70 pounds to the bulky, yet agile LSU star.
Mitchell, the lone senior starter for LSU, conceded that winning was a relief.
"We've been in the postseason three times - twice in the NCAA dance and once in the NIT - and we've exited the first round in all three of those events," Mitchell said. "So to get this win is a big weight off my shoulders."
Burtt and Soliver dominated early, giving Iona hope of getting its first victory in the NCAA tournament since coach Jeff Ruland was the team's star in 1980. The high-scoring tandem produced nearly 42 points a game during the regular season and combined for 24 of Iona's 37 in the opening half.
But once Davis took over, he was clearly the best player on the floor. His teammates fed off his energy from the moment he rebounded his own miss and scored for LSU's first basket of the second half.
Iona shot under 27 percent (8-for-30) in the second half and finished 3-for-18 from behind the 3-point arc.
"As a team they wore us down with their size," Ruland said. "Obviously 65 percent in the second half's not going to cut it. We had a period there where we had some open looks and missed them. That's when they got the lead and never relinquished it."