The 49ers played in front of a crowd of 18,854, according to ESPN, making them the second-largest audience for a Super Bowl broadcast in league history.
The 49ers, who are in the middle of a six-game winning streak, were led by quarterback Alex Smith, who completed 18 of 25 passes for 219 yards and three touchdowns.
Smith and safety Eric Reid both threw for touchdowns in the game, and Smith led the team in catches (nine), yards (2,907) and touchdown passes (23).
Reid added three catches for 38 yards.
The 49er defense forced eight turnovers, with only three coming on fourth down.
The win keeps the 49er franchise atop the NFL in total points scored (25,726), passing yards (1,769), passing touchdowns (12) and total offensive yards (4,062).
The 49-24 win also moved the 49-26 team in the NFC West to 3-0.
Smith is the first NFL quarterback to throw for 300 yards and five touchdowns in a Superbowl.
He joins Joe Montana (336 yards and four touchdowns in 1983), Peyton Manning (317 yards and one touchdown in 2013), Andrew Luck (317 yds and two touchdowns in 2012) and Andrew Luck Jr. (301 yds in 2011).
Reid also completed two of the three passes for touchdowns, including the game-winning one in the fourth quarter.