MIAMI -- Derrick Williams has officially started over.

Williams is signed with the Cavs for the rest of the season Saturday after playing out the last of consecutive 10-day contracts. He signed a $268,000 deal before Cleveland plays Miami at 8 p.m., the team that waived him in early February. He asked for the release so he could get that fresh start with the Cavs, and he's made the most of it.

"I kind of put myself in that position (of having to earn a contract)," Williams said Friday night, after the Cavs beat the Hawks 135-130. Williams scored nine points in 18 minutes, all on 3s, becoming one of an NBA-record six players on one team to make at least three 3s in a game.

"I put myself into a 10-day contract to really prove myself to the guys on this team," Williams said. "So far it's been great, been playing well. I've never been in that position since I've been in the NBA. I really wanted to really start over."

If you've become a Williams fan since he joined the Cavs on Feb. 9, you know his story now. He's a former No. 2 pick from the same draft in which Kyrie Irving was drafted first.

Williams has played on five teams in six seasons. He was struggling with the Heat when he asked Pat Riley for his release, then had his agent scare other clubs off from claiming him on waivers so he could come to the Cavs. In nine games, he's averaging 10.3 points, 3.1 rebounds and shooting 56 percent (43 percent from 3-point range). Williams is also averaging 24 minutes off coach Tyronn Lue's bench.

In other words, the Cavs wasted no time in putting the 6-8 wing to work, and he made the most of his opportunity.

"He definitely earned it," Lue said. "I felt that he (would sign for the season) before he even got here. Just playing against him on other teams and his motor, his athleticism, being able to guard four positions and he's shooting the ball well. He's come here and he's definitely earned it. He's played well for us."

The Cavs privately signaled almost from the moment they first brought him in that it was their intent to keep Williams for the rest of the season. This was not a decision that was reached after much deliberation or anything like that this week.

Nevertheless, Williams was anxious for this day to get here, when he could sign a guaranteed contract that would lock him into a team many say is bound for the Finals. Not because he needs the money -- he's earned $26 million over his career -- but because of the opportunity he sees on this kind of team.

LeBron James is here. Kyrie Irving. Kyle Korver. Kevin Love. The ball zips around. Players know their roles. Williams said it's different than any other place he's been.

It shouldn't come as a shock. The 25-year-old has never been to the playoffs or played for a team that finished with a winning record. Until now. By beating the Hawks Friday, the Cavs picked up win No. 42. They're guaranteed a winning record.

"Whenever you're on a championship level type team, everybody is helping each other," Williams said. "I think my previous teams maybe we lacked in that category a lot, where it's just about helping the next guy that's next to you, and once you get that, then the rotations start happening.

"It's just basketball's great here, when you see that it makes you want to join that and really pitch in."

Williams described a dizzying sequence from the second quarter Friday night. While he was on the bench, his teammates ripped pass after pass after pass around the perimeter, slinging the ball like it was a hot potato until Irving was alone for a 3-pointer.

The Cavs made an NBA record 25 3s in the game, and of course Williams played his part with his three treys.

It was in Cleveland's previous game against the Celtics when Williams drew the ire of James and teammates for passing up a 3 attempt in the fourth quarter. He was wide open in the corner, but instead of shooting he put it on the deck and was called for one of two consecutive charges that stunted the Cavs' momentum.

That was not going to happen against the Hawks.

"Whenever some of the best basketball players in the world tell you to shoot the ball, that just gives you so much more confidence," Williams said. "And I was mad at myself the other day against the Celtics, where I should've shot the open 3 and I drove and got a charge, so, I knew tonight I wasn't thinking about anything else other than knocking down the corner 3. And tonight I hit three of them."

His reward: A $268,000 payday that was coming whether those 3-pointers went in Friday night or not.