San Francisco did the damage on the ground rather than through the air, with Mostert being called in for 29 carries and gaining 220 yards and a quartet of scores.
The first scoring rush from 36 yards came 10 minutes into the encounter in California and was followed by a double in the second quarter as the home side went in 27-0 up at the midway point.
Aaron Rodgers connected with Aaron Jones for nine yards to put Green Bay on the board and two further touchdowns in the fourth were purely a consolation as the Niners advanced to their seventh Super Bowl.
Mahomes threw for three touchdowns and ran in another as the Chiefs secured a Super Bowl berth for the first time in 50 years.
A 27-yard rush from the quarterback towards the end of the first half gave the Chiefs a lead they would not relinquish in Missouri.