Tinsley's milestone is more impressive because he's played only 110 NBA games since the end of the 2006-07 season.
He did not play last year and was signed by the Jazz as a free agent in the offseason.
"Sometimes it's all about how you respond to adversity and he's done an incredible job for us," said Jazz general manager Kevin O'Connor.
"He's one of the harder working guys on our team. He kept himself in incredible shape waiting his turn and, when the opportunity presented itself, he delivered."
Tinsley, 34, averages 3.8 points and 3.2 assists in 13.2 minutes this season.
He had been Utah's No. 3 point guard behind Devin Harris and Earl Watson. But he became Harris' primary backup after Watson suffered a season-ending knee injury.
"Wet willy" aftermath
The morning after Delonte West stuck a finger in his ear during Utah's 123-121 triple-overtime win over Dallas, Gordon Hayward admitted his first instinct was to confront the Mavs' veteran guard.
Instead, he walked away.
"You have to keep your composure more than getting into a fight or anything like that," Hayward said.
The incident began when West fouled Hayward as the two ran up the floor. West kept talking to Hayward and, at one point, stuck a finger in his ear.
After reviewing the play on TV, the officials gave West a technical foul but, strangely perhaps, did not eject him for an incident that could have triggered something worse.
Said Hayward, "He bumped me and it's like, 'O.K., he's obviously frustrated.' Then, when he did the second [thing], it's like, 'Man, we've got him right where we want him.'"
According to Hayward, the Jazz "got the last laugh" by beating the Mavericks.
West could be facing disciplinary action by the NBA, which Hayward's teammates criticized.
" ... I thought it was childish," Jeremy Evans said. "But, as far as Gordon, I thought he was really strong keeping his composure. A lot of guys really can't do that."
Said rookie Alec Burks: "There's no call for that. I mean, we're all grown men. You can't challenge somebody's manhood out there like that. I didn't like that at all."
Asked if he's ever seen anything like it, Burks said, "In pick-up ball, it happens a lot. But we're out here playing a game and we get paid for it. There ain't no need for that."
Jazz sorting out Orlando summer league roster
The Jazz will send a team to the Orlando Pro Summer League on July 9-13.
O'Connor hopes Utah's summer roster will include "all our young kids. But we'll have to wait and see exactly who that is."
Derrick Favors, Enes Kanter, Hayward and Burks seem to be strong possibilities for Orlando. So do Evans and DeMarre Carroll, if the Jazz can re-sign him.
If Jazz make playoffs, they could have Bell
The 12-year veteran is recovering from a left knee injury. He received a hyalgan injection April 2 and was ruled out indefinitely at the time.
Bell's recovery has gone well and he resumed running and minor basketball-related activities Monday.
"If I can get into shape and situationally … I can help, I'm all up for it," said Bell, who hasn't played since March 15, and also dealt with a groin injury this season.
Bell, 35, is averaging 6.6 points in 33 games (all starts), while shooting 47.9 percent from the field and 40.5 percent behind the 3-point line.
Bell said he understands Utah has a "good thing going" right now, and will allow Corbin to determine his role moving forward.
"They're cooking, so you don't want to get in there and screw everything up," Bell said.