Ramirez allowed three runs on just five hits, walked two and struck out six in seven innings.
"That's one of the best seven innings we've had from our young guys this season, if not the best," said manager Dusty Baker. "He gave us what we needed. He certainly deserved the victory."
The Giants denied Ramirez his first career win with a three-run rally which tied the score in the eighth. But Corey Patterson's triple in the bottom of the inning scored Jay Bruce from first with the eventual winning run.
Edwin Encarnacion hit his 24th home run of the season, helping the Reds win two consecutive games for the first time since July 22-23.
"The important thing was to win the game," said Ramirez, through bullpen coach Juan Lopez, who interpreted. "I was feeling nervous in the first inning. I relaxed after that. I tried to mix up my fastballs and changeup. Both were working pretty good."
Randy Winn greeted Ramirez with a solo home run into the right-field seats, putting the Giants ahead, 1-0. It was Winn's third leadoff homer this season.
Solid situational hitting, not the Reds' strong-suit this season, helped them regain the lead in the first.
Chris Dickerson, who fell a triple shy of the cycle in Friday night's win, began the inning by tripling into the right-field corner. He scored on Jeff Keppinger's sacrifice fly to right, tying the score at 1.
Later in the inning, Brandon Phillips singled and scored on Encarnacion's sacrifice fly to put the Reds ahead, 2-1.
Reds batters continued to pound Giants starter Kevin Correia. Patterson delivered an RBI single to make the score 3-1. Ryan Hanigan's two-run double increased the Reds' advantage to 5-1.
Eugenio Velez's first career home run, a two-run shot off Ramirez in the second, made the score 5-3. Correia (3-8) allowed six earned runs on seven hits in six innings. He walked two and struck out two.
In the third, the Giants had runners on first and third, but Ramirez fanned Aaron Rowand to end the inning.
Encarnacion's solo homer in the third made the score 6-3.
Encarnacion has hit safely in six of his past eight games, including home runs in consecutive days. He's batting .321 in that stretch.
Ramirez retired 10 of the final 11 batters he faced, including three consecutive hitless innings.
"He pitched well for his first outing," said Hanigan, who caught Ramirez on a few occasions in the Minor Leagues. "I'm sure he was a little nervous. He started to get a feel for his changeup. He settled down after the first couple innings."
Although Ramirez was cruising with 98 pitches through seven innings, Baker chose to summon the bullpen. Winn greeted Bill Bray with a solo homer, his second of the night, making the score 6-4.
Fred Lewis scored from third on a double-play grounder, then Rowand tied the score with a solo home run off Mike Lincoln. It was Lincoln's first blown save of the season.
"Lately, they've been struggling a bit," said Baker of the bullpen.
The Reds rallied back when Bruce singled with one out in the eighth, and raced home from first when Patterson laced a triple to center, putting the Reds ahead, 7-6.
Despite his blown save, Lincoln (2-5) earned the victory. Jack Taschner (3-2) took the loss for the Giants.
Francisco Cordero pitched a scoreless ninth for his 26th save, but not without drama.
Lewis sent a deep drive to center field, but Patterson made the catch with his back against the wall.