It was also the first time all of the Dodgers' hits were home runs since 2002 against the Angels.
Starting pitcher Aaron Harang shook off a first-inning run to deliver another quality start, charged with that one run on four hits in 6 2/3 innings to raise his record to 9-7, striking out eight while walking five.
Ramirez did the heavy lifting, as he has pretty much since arriving before the Trade Deadline. In 23 games with the Dodgers, he has four homers, 27 RBIs and a .330 average.
"The last couple of years, he's put a lot of pressure on himself," Harang said of Ramirez. "He comes here and between him and Andre Ethier and Matt Kemp, they keep the pressure off him and he keeps the pressure off them. He seems to be having a good time and he's really loose on the bench."
"I don't have to try to be the better hitter," he said. "We've got so many guys that can beat you. From my first day, [coach] Manny Mota talked to me and gave me a lot of confidence. Everything he tells me I try to do."
The last time a Dodgers pitcher enjoyed the support of three consecutive homers, he had to hit one himself. That was June 12, 2007, when Wilson Betemit, Matt Kemp and then-starter Hong-Chih Kuo took John Maine of the Mets deep. Kuo finished the trifecta with his infamous bat flip.
The showboating this time was Ramirez's "I see you" gesture, but he waited until he was nearly back to the dugout, unlike earlier this month in San Francisco when he did it rounding second base on his home run trot. He repeated the celebration after his three-run shot, the Dodgers' only at-bat with a runner in scoring position.
Ramirez evened the score at 1 in the second inning on his home run to center. Loney made it back-to-back two pitches later and Cruz made it back-to-back-to-back on the next pitch.
Loney, who went 67 games without a home run, has two in the last three games. Meanwhile, including a three-hit game Friday night, Cruz is 11-for-25 on the trip with six RBIs and five extra-base hits.
Except for that four-pitch span, Sheets was perfect for 5 2/3 innings. He retired the first four batters before the three homers, then retired the next 13 batters. But with two outs in the sixth, he walked Kemp, who stole second base during a walk to Ethier, then Ramirez drilled a liner into the left-field stands.
The Dodgers were 1-for-1 with runners in scoring position and left one runner on base. The Braves were 0-for-9 and stranded 11.
"That was a weird game," Braves catcher David Ross said.
While the four RBIs from Ramirez were the difference, acting manager Trey Hillman credited Harang, who walked three in the first inning but escaped with only one run allowed.
"The key for me was getting out of the first inning," Hillman said of Harang, who struck out Ross on a foul tip with the bases loaded and two outs.
Hillman, Mattingly's bench coach and former manager of the Kansas City Royals, had to do some maneuvering of pitchers with his boss serving the first of a two-game ban for Thursday's ejection.
In the seventh inning, with two outs and a runner on third, Hillman lifted Harang to bring on lefty Randy Choate, who struck out lefty Jason Heyward. Friday night in the eighth inning, Mattingly didn't bring in Choate and Heyward tied the game with a single off right-hander Ronald Belisario.
In the eighth inning after Javy Guerra walked two of the first three Braves and went 2-0 to Ross, Hillman brought on Shawn Tolleson, who got Ross to foul out.
"It wasn't an easy decision for me," Hillman said. "Back when I had a different job, full-time managing, I very seldom took a guy out in the middle of a count. But the determining factor was Javy was just missing too far from the zone."
Tolleson then walked Paul Janish to load the bases and Hillman called on Kenley Jansen for a four-out save. Jansen extinguished the eighth-inning jam by striking out Juan Francisco, whose walk-off hit the night before against Jamey Wright won the game for the Braves.
"Nicely done," Mattingly said as he walked past Hillman while he was speaking to reporters.