Dawson had also given the 49ers a 20-17 lead with 1:45 left in the fourth quarter, but the Cardinals came right back with a Jay Feely 43-yarder to knot the score 20-20.
San Francisco (12-4) had a chance to win its third straight NFC West title, but settled for the NFC's fifth playoff seed after Seattle bested St. Louis for the division crown Sunday.
The Niners will play NFC North champion Green Bay in the wild card round.
Carson Palmer completed 28-of-49 passes for 407 yards, two TDs and an interception for Arizona (10-6), which saw its playoff hopes evaporate when New Orleans routed Tampa Bay earlier Sunday.
2014: The Year in Music [PHOTOS]