Frazier swung at the first pitch he got from Greinke and hit a two-run homer on Thursday afternoon, sending the Cincinnati Reds to a 4-1 victory over the Los Angeles Dodgers and a split of their four-game series.
The Reds won the last two games to finish a 5-5 homestand that left them stuck closer to the bottom of the NL Central than the top.
Alfredo Simon (9-3) gave up seven singles in eight innings, joining the Cardinals' Adam Wainwright as the NL's nine-game winners.
Greinke (8-3) had been 4-0 in five games at Great American. A slow start cost him his perfect mark. Skip Schumaker opened the Reds' first with a single, and Frazier followed with his team-high 14th homer on Greinke's fifth pitch of the game. Joey Votto doubled on the next pitch as well.
''I was just trying to electrify us and get us going,'' said Frazier, who has five homers in his last 11 games. ''First pitch, I was ready to attack. It was good to get the lead for Alfredo.''
Greinke gave the third baseman credit for hitting a pitch that ended up where it was intended.
''It wasn't necessarily any worse pitches than the rest of the game, just that Frazier's hot,'' Greinke said. ''A first-pitch slider at the bottom of the zone, you take your chances. But he's a strong guy and got a homer out of it.''
Cincinnati would get only one more hit off Greinke, who went six innings before leaving for a pinch-hitter.
Simon matched his career high with eight innings and held the lead by pitching out of a threat in the seventh with a 2-1 lead. Matt Kemp and Andre Ethier opened with singles. Tim Federowicz flied out too shallow to score the run, and Kemp was caught in a rundown after he tried to score on Miguel Rojas' grounder. Pinch-hitter Scott Van Slyke struck out to end the threat.
''What he's he doing that's most surprising to me is pitching effectively into the seventh and eighth innings,'' manager Bryan Price said. ''He's pitching deep into games and continuing to stay aggressive with his stuff. He looks very comfortable in high-leverage situations.''
The 33-year-old pitcher has been a reliever most of his career, but embraced the chance to start. So far, he hasn't shown any problems making the switch.
''I feel like my arm is only 20 years old,'' Simon said. ''I feel like I can throw 200 innings.''
Aroldis Chapman pitched the ninth for his 10th save in 11 chances.
Simon's nine wins match his total for his last two seasons with Cincinnati, when he was a reliever. Simon moved into the rotation when Mat Latos tore knee cartilage and had surgery at the start of spring training. Latos is expected to bump left-hander Tony Cingrani from the rotation when he returns from the disabled list this weekend.
The Reds' offense was finally back together during the homestand, with Votto returning from a strained muscle above his left knee that landed him on the disabled list for 23 games. Votto had a double and a single on Thursday, leaving him 4 for 10 in his three games back.
The Dodgers completed a 4-3 trip to Colorado and Cincinnati, two hitter-friendly ballparks. Their pitching was solid, but the offense faded at the end, scoring one run in the last two games. They were limited to eight singles on Thursday, including Kemp's RBI hit in the first inning.
The Dodgers start a six-game homestand on Friday against Arizona. LHP Clayton Kershaw (5-2) faces Chase Anderson (5-0). ... The Reds play their next six games in Milwaukee and Pittsburgh. Homer Bailey (7-3) faces Matt Garza (4-4) on Friday. ... LA is 39-22 against the Reds since the start of the 2006 season. .... The Dodgers won a challenge in the first inning, when Brandon Phillips initially was called safe at first base. The replay showed he was out. ... SS Hanley Ramirez was out of the lineup for a second consecutive game with a sore throwing shoulder. He got an injection after Wednesday's game. ... Phillips left in the eighth inning with a sore right index finger, hurt on a defensive play earlier in the game. ... Cozart extended his hitting streak to seven games.