The calendar may have turned to 2013, but apparently the Massachusetts men’s basketball team’s New Year’s resolution wasn’t to eliminate nail-biting victories.

Its most recent case came Wednesday night when UMass trailed at Miami (Ohio), 69-68, with less than 90 seconds remaining. Chaz Williams drove to the lane and sunk a floater with 1:12 left to give the Minutemen a one-point advantage.

Quinton Rollins followed up by missing the front end of a 1-and-1 for the RedHawks the next trip down the court that could have tied the game or given them the lead had he made the ensuing free throw. Instead, UMass (9-3) squeaked out a 70-69 victory to secure its third game decided by three points or less.

“I was just creating a play,” Williams said of his game-winning shot in a postgame interview. “The game was close, clock was running down, and coach looked for me to be aggressive and make plays, so that’s what I wanted to do.”

Will Felder made a pair at the charity stripe to give Miami a 69-68 lead with 3:28 left, but both sides went scoreless for the next 2:16 before Williams’ go-ahead jumper finally broke the scoring skid.

Raphiael Putney led the way with his season-high 20 points to go along with nine boards and three steals. Williams finished just shy of a double-double (10 points, nine assists), while Maxie Esho swatted four shots in the first half and corralled nine rebounds of his own.

Allen Roberts had 21 for the RedHawks (5-7), but didn’t score in the final 7:18, taking just two shots during that span.

Despite their six-game winning streak, the Minutemen haven’t had any easy victories, as each of their nine wins have been decided by single digits with an average margin of victory of 4.3 points.

Putney acknowledged the team’s close contests when speaking after the game, but feels the late-game victories are building up to Atlantic 10 play, which starts Jan. 10 at Saint Louis.

“We should be beating these teams by double digits, but conference play is coming around, and we’re building up a strong brotherhood so we can get these W’s in conference play when it matters the most,” Putney said.

UMass took a 37-29 lead into halftime, but Miami stormed out of the locker room with a 13-5 run in the first 2:29 of the second half to knot the score at 42.

Neither team could muster any sort of momentum after that, as both teams matched each other basket for basket. The largest lead of the final 15 minutes was four (Miami).

The Minutemen weren’t shy about firing shots from beyond the arc, finishing 11-for-33 in the contest. UMass coach Derek Kellogg felt the 33 attempts was too many.

“When we stopped shooting 3’s, that’s when we built our lead,” Kellogg said. “I thought we settled a bit. The games where we’ve shot way too many are the games where we haven’t really scored as much as I would like.”

Williams agreed the Minutemen took too many 3’s, but said the total had to do with the RedHawks inviting them to take shots from long range.

“That’s what they were giving us,” Williams said. “We have to take what the defense is giving us.”

Putney’s 20-point showing marks the first time he’s scored in double digits in the last nine games. Putney had struggled mightily heading into the game, averaging just over six points per game before hitting 8-of-19 shots on Wednesday, including 4-of-10 from downtown.

Putney said his energy and teammates’ faith helped with his breakout game, but the biggest factor was something simple: sleep.

“I slept real good last night, and I just came and played today,” Putney said. “That was the biggest thing. I’ll sleep better tonight. There’s a lot of burden off my shoulders.”

Jesse Morgan added 12 points, but struggled in the contest, shooting 5-of-18 from the field and 2-of-10 from the 3-point line.

UMass wraps up its non-conference schedule Saturday afternoon at the Mullins Center when it takes on Eastern Michigan. Tip-off is at 2 p.m.

Stephen Sellner can be reached at [email protected] and followed on Twitter @Stephen_Sellner.