Packers coach Mike McCarthy said he was aware of the mistake, but chalked it up to being "part of the game."
The Packers tied the game at 21 in the third quarter when Rodgers connected with Jordy Nelson for an 8-yard touchdown pass.
Davis made a pretty, reaching 37-yard catch on San Francisco's ensuing drive. Matthews sacked Kaepernick for a 7-yard loss and the Niners settled for a 27-yard field goal by Dawson, who hooked a 48-yard attempt wide left earlier.
Rodgers rallied the Packers for a 76-yard drive that Lacy capped with a 2-yard TD run before Kaepernick and the 49ers came back one last time.
Notes: Brad Jones led the Packers with 10 tackles. ... Matthews' sack was the only one for Green Bay. ... Aldon Smith had 1½ sacks against Rodgers after getting a franchise-best 19½ all of last season.