SALT LAKE CITY -- Al Jefferson hasn't been close to the playoffs since his rookie season.
Seven years later, the Utah Jazz big man is doing everything he can to make sure he's not on the outside looking in again.
Jefferson scored 28 points and tied a career high with 26 rebounds to fuel Monday night's 123-121 triple-overtime victory over the Dallas Mavericks.
"Right now we just got to win every game, no excuse," said Jefferson, who had 10 points in the extra periods. "This is a big test for us. We just got to see where our heart is, and I know everybody in the locker room wants to make the playoffs. So we are going to fight and we are going to fight 'til the end. That's all we can do."
Dallas was coming off an overtime loss Sunday to the Los Angeles Lakers, and Monday's felt just as bad. It was the Mavs' first triple-OT game since Dec. 29, 1989, against Portland, which they also lost.
"It's a disappointing loss," said the Mavs' Rick Carlisle, coaching his 800th career game. "We have to get ready for the next one. There's not a lot of time to belly ache. It was a phenomenal game, the competition was great, but we came up short."
Monday's win halted Utah's seven-game losing streak against the Mavericks but more importantly kept the Jazz in the postseason race.
Utah began the day 10th in the Western Conference but pulled one-half game behind Phoenix and Houston for the eighth and final spot with four games remaining.
The Jazz (32-30) hold the tiebreaker with the Rockets but not with the Suns, who they face again next week.
The loss dropped defending champion Dallas to seventh in the West, one-half game behind Denver.
Dirk Nowitzki scored 40 points against Utah for the second straight time. His 3-pointer forced the second overtime, but he couldn't convert late in the third extra period.
The Jazz forced overtime on Paul Millsap's putback dunk with 2.2 seconds remaining in regulation.
"The good thing about the overtimes is we knew they were going to kind of run out of gas," Jefferson said. "They are an older team, they played yesterday. So we knew the shots were going to start falling a little short. I am surprised they lasted as long as they did."
The Jazz led by as many as 11 points early and were up 87-83 with 46 seconds left in regulation before Vince Carter hit back-to-back 3s, including the second with 8.5 seconds left in regulation.
On Utah's final possession in regulation, Gordon Hayward drove the lane but missed only to have Millsap fly in for thunderous putback dunk.
Nowitzki's long 3 to win it at the buzzer in regulation came up short.
Utah led by four in the first overtime only to see Nowitzki force the second extra period with a 3 with 3.9 seconds left.
Jefferson hit a jumper in the third overtime then blocked Ian Mahinmi's shot, setting up Millsap for a fast-break score and 115-113 lead.
Devin Harris hit a 3 and Jefferson's 6-foot running jumper after Nowitzki's missed 3 gave Utah a 120-115 lead with 1:08 remaining.
Delonte West sank a 3 with 56 seconds left to get Dallas back within two points.
Millsap made 1 of 2 free throws with 14.9 seconds left and Utah led, 121-118.
Jason Terry and Nowitzki both missed 3s in the final 10 seconds. Terry finished with 27 points and four 3s.
Harris' free throws provided Utah's final points before West hit a 3 that was too little too late.
"Big plays and big shots on both ends of the floor, the crowd was into it, so you couldn't ask for a better game," said Nowitzki, who added nine rebounds and six assists. "We had our chances. If we get one rebound at the end of regulation, the game is over."
DeMarre Carroll instead would come up with two huge rebounds for the Jazz late in the third overtime.
Carroll was playing just two days after having a front tooth dislodged and suffering a mild concussion in a loss at Memphis.
He was cleared to play Monday morning and finished with 15 points, four rebounds, six assists and a steal for the Jazz.
Hayward added 24 points for Utah and Harris had 23, with five 3s.
Like the last game played in Utah between the teams, this one got chippy, with the Mavericks whistled for three individual technical fouls.
West drew chants of "Throw Him Out" after he was called for a technical in the second quarter after fouling Hayward away from the ball then poking his index finger in the back of Hayward's head a few seconds later.
Nothing was more physical than the matchup between Nowitzki and Millsap, who bumped and battled the entire night.
"He's a tough player," said Nowitzki, who started 3-of-3 but found early foul trouble. "I always liked him. He can make plays off the dribble and can post up. He's an active defender. We always have good matchups. Just their whole team competes. I don't care who they throw out there."
Millsap finished with 16 points, nine rebounds and two blocks.
No matter how tight the Western Conference race, the Jazz know how hungry Jefferson is.
"He was huge," Jazz coach Tyrone Corbin said. "I mean 26 rebounds, the timely shots on the perimeter. They were double-teaming him as soon as he got it, had bodies on him all night to try to get him off the block. But he hung in there."
Mavericks PG Jason Kidd was making his 1,300th career start and his 498th with Dallas. ... Terry tied the Clippers' Chauncey Billups for fourth place on the NBA's career 3-pointers list at 1,783. ... Jazz SF Josh Howard (knee surgery) and SG Raja Bell (knee) both worked out for about 15 minutes on the court during Monday's morning shootaround. ... Jazz backup PG Earl Watson will undergo surgery Tuesday in New York to repair torn cartilage in his right knee. ... NBA D-League call-up Blake Ahearn scored his first Jazz points on a 3-pointer with 11:43 left in the second quarter.