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SALT LAKE CITY — So what if the Boston Celtics were playing the final game of a five-game road trip a night after losing in Portland and were without star point guard Rajon Rondo, who is out with a knee injury?

All the Celtics needed were their two cagey vets, Paul Pierce and Kevin Garnett, who carried their team to a 110-107 overtime victory over the Jazz on Monday night.

The 34-year-old Pierce and 35-year-old Garnett scored the first 11 of the Celtics’ 13 overtime points in what was Boston’s fifth straight victory over the Jazz. It left the Jazz and their fans deflated, although a good portion of the EnergySolutions crowd — the noisy folks in green Celtics jerseys — went home happy.

After a slow start for both teams, Pierce and Garnett came through when it counted against a Jazz team that played three young reserves — Alec Burks, Gordon Hayward and DeMarre Carroll — down the stretch of regulation and in overtime. In the OT, Pierce was 3 for 3, while Garnett was 2 for 2. Pierce finished with a game-high 26 and Garnett added 13.

“Paul, down the stretch, just carried us,’’ said Boston coach Doc Rivers. “'Feed the pig,' I kept yelling, ‘feed the pig.’ He had it going, so feed him.’’

Rivers had been concerned about his team, particularly his veterans, playing their fifth game in seven nights. So before the overtime, he told Brandon Bass to go in for Garnett.

“I told Brandon go in for Kevin, but Kevin wouldn’t let me. He said, ‘No, no, I’m good.’ I didn’t believe that but I kept him in and he was terrific.’’

Garnett got the Celtics rolling with a jumper at the start of the overtime. After two Jazz baskets gave the Jazz the lead at 101-99, it was Pierce’s turn as he knocked down a 3-pointer from out top to give the Celtics the lead for good.

Pierce hit two more jumpers to give the Celtics a 106-101 lead and after Al Jefferson scored for the Jazz, it was Garnett’s turn as he scored on a 15-footer to push the lead to five again.

Garnett made another basket, but it came just after the shot clock expired and the Jazz were able to close within one with 4.2 seconds left. However Courtney Lee hit a pair of free throws at the 1.2-second mark and Utah’s Randy Foye couldn’t force a second overtime.

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Afterward, Pierce tried to deflect attention from himself, calling it a team effort and praising Boston’s young guards, Avery Bradley and Lee, who scored 18 and 14, respectively. He talked about his mindset in the overtime

“Just stay aggressive and take the shots that are there,’’ he said. “I thought I got a good look — sometimes they fall and sometimes they don’t. Usually in overtime on a long road trip, you can kind of give in mentally. ... But this team showed tremendous fight, dug in and did what it had to do.’’

Rivers called the win the “best of the year’’ for him.

“We came in on fumes and we hung in there and hung in there,’’ he said. “This says a lot about our team.’’