The Giants became the first team to win a division series after losing the first two games at home and they will now take on either Washington or St. Louis for the National League pennant.
The Nationals evened their division series with the Cardinals at 2-2 thanks to a 2-1 win in Washington Thursday.
Mat Latos started for Cincinnati, having thrown 4 1/3 innings of relief in the opener of the series after Johnny Cueto suffered an injury in the first frame.
Latos worked out of a first-inning jam on Thursday and appeared to settle in after that while allowing a lone hit during the second, third and fourth.
Things unraveled in a hurry in the fifth, however, when Gregor Blanco led off the inning with a single and promptly scored the game's first run on a Brandon Crawford triple.
After pitcher Matt Cain grounded out, Angel Pagan reached base on a fielding error at shortstop by Zack Cosart that allowed Crawford to score.
Cincinnati outhit San Francisco 12-9. The Reds have not won a post-season series in 17 years.
The Giants will be playing in their sixth NLCS, having last done so two years ago when they went on to win the World Series.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys