Wright posted a score of 89.5 and earned $17,512.
After finishing second twice and fourth once in earlier rounds, Wright bumped his NFR earnings to $50,840 about $5,000 less than he previously earned this year.
Meanwhile, the other Wright brother competing in the NFR did not complete his ride Monday.
Cody Wright had won Rounds 2 and 3 and tied for second in Round 4, but he finished out of the money in the fifth round with a score of 81.5.
It was a tough night for Utah's other four NFR participants, too.
In bareback, Kaycee Feild, of Payson, did not complete his ride and failed to post a score.
In the previous four rounds, Feild won twice and tied for third place once. He has already earned $43,921 at the National Finals.
In bull riding, neither Wesley Silcox, of Santaquin, nor Steve Woolsey, of Payson, completed their eight-second ride.
In fact, only three of the 15 bull riders posted scores, led by Round 5 winner J.W. Harris, who had an 89.
In barrel racing, Kelli Tolbert, of Hinckley, was timed in 14.03 seconds, which was not good enough for a money-winning finish.
The National Finals Rodeo continues nightly through Saturday.