SALT LAKE CITY -- "Determination over negativity" isn't just a marketing slogan for Donovan Mitchell's Adidas signature shoe. It's a mantra for the young Utah Jazz star.

So Mitchell wasn't thinking about how much he had struggled during this Western Conference playoff series when the fourth quarter of Game 4 began with the Houston Rockets leading by four points. He just wanted to make sure the Jazz got to board a flight to Houston the next afternoon.

"I'm not trying to go home," Mitchell told ESPN after scoring 19 of his game-high 31 points in the fourth quarter of the Jazz's series-extending 107-91 win Monday night. "I'm not trying to watch the rest of these games from the couch."

Mitchell made sure the Jazz's season didn't end by single-handedly outscoring the Rockets 19-12 in the final quarter. He had a flurry of 13 points during a 15-1 run in the first few minutes of the frame that gave Utah the lead for good.

Mitchell struggled mightily as the Rockets put the Jazz in jeopardy of being swept, shooting 32.8 percent from the floor in the first few games of the series, including missing a wide-open 3-pointer that would have tied the score in Game 3 with eight seconds remaining. Mitchell's misery continued for most of Game 4, as he missed nine of his first 12 shots from the floor.

Mitchell started to warm up when he made a couple of driving layups in the third quarter, just before he got a breather for a few minutes at the end of the period.

"That's when I realized that I had to continue to be aggressive," Mitchell said. "I thought they were fouls, and they weren't, and I've got to be able to fight through contact. I said, 'All right, you're not getting nothing. You've got to be able to be even more aggressive.'"

Mitchell came out firing to start the fourth quarter, with Rockets guard Eric Gordon, his nemesis all series, resting to begin the period. Mitchell swished a 3-pointer from the left wing off a feed from Ricky Rubio on the first possession. After a Rubio floater gave the Jazz a lead, Mitchell scored 11 consecutive points -- hitting a pretty turnaround jumper after a spin move in the lane, knocking down a pair of free throws, getting a shooter's roll on a 30-footer in transition and punctuating the run with a pull-up 3.

"The confidence level goes from zero to 100," Mitchell said. "Well, I wouldn't say zero, but it just goes up crazy. For me, the biggest thing is maintaining your composure. Not just going to shoot because you can, but being able to make the right plays. I think what I was most happy with was that I didn't settle. I kept getting into the paint.

"My teammates obviously just having my back is huge, continuing to fight, fight, fight and just [encouraging me] to take the same shots I've been taking, not shying away because of my struggles."

The Jazz had been outscored by 11 with Mitchell on the floor through the first three quarters. He was plus-19 in the fourth quarter, when he was 6-of-12 from the floor, 3-of-5 from 3-point range and 4-of-4 from the free throw line.

"We made some mistakes," said Rockets coach Mike D'Antoni, whose team was 4-of-20 from the floor and 0-of-13 from 3-point range in the fourth quarter. "Left him one time on a penetration and he hits a 3. We didn't square up on another penetration, it's a layup. Just, it's us. I mean, it's him, too. I mean, he's good. He's gonna get rolling, so I'm mot worried about that if we do what we're supposed to do, but we didn't."

Mitchell scored more points in Monday's fourth quarter than he had in the final frames of the Jazz's three losses in the series. He had 13 points on 4-of-16 shooting in the first quarter of the previous three games.

"We know he's a winner," said Jazz center Rudy Gobert, who along with Derrick Favors anchored a dominant defensive performance. "It was hurting him a lot, too, after those bad games. I knew that he was gonna come out ready tonight, and he did."

Jazz reserve guard Kyle Korver felt so strongly about Mitchell after Game 3 that he made a lengthy statement without prompting in support of the second-year guard, saying he'd never seen anyone as young as the 22-year-old take ownership of a team with such charisma and class. Korver said then that the missed 3 that would have tied the game would just be part of Mitchell's journey.

Now, so is a spectacular scoring flurry in the fourth quarter to help the Jazz avoid a sweep.

"Anyone who's spent any significant amount of time with him knows that his character is as high as his talent level," Korver told ESPN. "Things happen in playoff series. We're all on this learning curve. He's early in his postseason career. It's only his second year, but this is who he is. Tough night the other night, right? It was a hard one, but we all knew that he was going to bounce back.

"And he didn't start off this game well. He didn't really get going until the fourth quarter, but every single person in our locker room had confidence that when the game was on the line, he was going to take the shots and he was going to make them."