Harang, who struck out eight and issued an intentional walk, has allowed two earned runs or fewer in five of his six starts and has a 1-3 record to show for it.
He did move into the NL lead with 37 strikeouts, one ahead of both Tim Lincecum and Friday's winner Jonathan Sanchez.
The Reds have lost three straight and 11 of 14 overall. Edwin Encarnacion went 0-for-3 and had his career-high 14-game hitting streak snapped. The Reds still haven't won the first game of a series, dropping to 0-9 in such situations.
"That was an outstanding game," Reds manager Dusty Baker said. "Aaron pitched outstanding. He didn't want to come out of the game. There was also a young man on the other side who threw a great game. He located his fastball low and away and he threw that fastball in the 'T' zone where it looked like a strike, but not when you swung through it."
While the Reds haven't been scoring runs in bunches, they've averaged 4.3 a game over their past 10 games. And there are seven teams that have scored fewer runs, including the Giants.
"You have to give the other guy credit," Harang said. "This was definitely a pitchers' game where one little mistake can cause everything to tumble out."
Bengie Molina drilled a double into the right-center-field gap to drive in the first run of the game, with two outs in the fourth, and Harang didn't consider that a big mistake.
"He did a good job of going the other way with it," Harang said. "I felt like I went out and hit my spots and kept the mistakes to a minimum. I'm trying to keep my walks down and make them put the ball in play."
Ryan Freel led off the game with a single and was wiped out on a baserunning mistake. The Reds didn't get another baserunner until Harang doubled with two outs in the sixth.
Sanchez retired 16 straight between the hit by Freel, who added a hit in the ninth to end Sanchez's night, and Harang's double.
"The pitching we're going up against -- [Greg] Maddux, then Chris Young, then Harang -- you need your guy to go out there and put up zeros," Giants manager Bruce Bochy said. "They responded and all of them have thrown the ball great, these starters. They are giving us a chance."
The Reds finally got a runner as far as third in the seventh when Encarnacion was presented with a walk, stole second and rambled into third on a fielding error. That also came with two outs.
Brandon Phillips broke up the shutout with a pinch-hit homer leading off the ninth against Sanchez.
"Brandon hasn't been swinging well lately," Baker said. "Maybe Brandon will get going. He was aggressive and looked like the Brandon I know."
It was Phillips' first career pinch-hit home run.