Smith competed 18-of-31 passes and Gore gained 65 yards on 18 carries for playoff-bound San Francisco (11-3), which is seeking to secure a first-round bye in the post-season.
The game was interrupted twice by power outages at Candlestick Park.
Pittsburgh quarterback Ben Roethlisberger was doubtful for the game due to a high ankle sprain, but shook off the injury to make the start.
He passed for 330 yards on 25-of-44 efficiency, but committed four turnovers for the Steelers (10-4), who saw their four-game winning streak snapped and failed to take advantage of an opportunity to grab sole possession of first place in the AFC North -- created when Baltimore fell to San Diego Sunday.
Swim Week Miami Beach 2014 [PHOTOS]