The Nuggets waived Carroll after he played in only four games with them last season.
The Jazz signed Carroll in February and, since then, he has solidified his spot on the roster with the kind of performance he turned in against the Nuggets.
"I knew I could contribute [to] their team," Carroll said. "But the Jazz have faith in me and look at me now."
Jazz coach Tyrone Corbin played against former teams many times during his 16-year NBA career, so he knows how Carroll felt.
According to Corbin, such a performance is "absolutely" special because "you feel good about who you are and where you are and your growth in the league. ... His defense really helped us in the second half."
The Jazz owned a 102-100 lead with 1:28 left when Denver's Danilo Gallinari tried to tie the game. Carroll stayed in front of him, however, and forced Gallinari into a tough shot.
It didn't come close.
"Just solid 'D,'" Carroll said.
Referring to former Memphis teammate Tony Allen, who is known as one of the league's top defenders, Carroll added, "My mentor, Tony, taught me to play solid 'D' and that's all I try to do.
"I'm not going to change the game in an offensive way like Gordon [Hayward] or Al [Jefferson] or Paul [Millsap]. But I'm going to affect it on the defensive end and I knew that was my prime time when I had him one-on-one to show everybody I'm a defensive stopper."
Corbin used Hayward and Carroll instead of Randy Foye and Marvin Williams in the fourth quarter because the switch provided the Jazz with defensive flexibility against the Nuggets.
"This team is capable of scoring points in a hurry so, once you get them in a place where they are struggling, you want to stay with it," Corbin explained.
"We just decided to stay with the group we had [because] they did such a good job on the defensive end. But I thought Randy and Marvin did a good job in the third quarter."
Carroll stops Denver
• Utah's DeMarre Carroll plays 23 minutes against Denver, including all but 24 seconds of the fourth quarter.
• The Nuggets made only six of their final 19 shots, including 1 of 5 in the final two minutes.