Dawson hit a 56-yard field goal to put San Francisco ahead with 1:45 to play on Sunday at Arizona and then booted a 40-yarder as time expired to win it.
He was also honored by the NFL in Week 14 after making all four of his field-goal attempts in the 49ers’ 19-17 win over the Seattle Seahawks.
He also hit a 27-yard field goal in the first quarter of the game. He did miss one from 24 yards out in the second quarter to snap his franchise-record streak of 27 consecutive makes.
In his first season with the 49ers, Dawson was 32-for-36 on field-goal tried and made all 44 of his extra-points, finishing with 140 points, the second-highest total in club history behind the 166 by David Akers in 2011.
Dawson spent the first 14 years of his career with the Cleveland Browns and is 13th all-time with an 84.5 percent success rate. His 337 field goals is 18th-most in NFL history and he is 26th on the all-time scoring list with 1,411 points.