Ramirez ended a pitcher's duel between Chad Billingsley and Brandon Webb with a three-run homer off Webb in the fifth and later added a two-run double in the sixth on a ball Justin Upton lost in the sun to extend the lead to 7-0.
The homer, No. 521 in his career, put him in a four-way tie with Willie McCovey, Ted Williams and Frank Thomas for 17th all-time and the RBIs pushed him past Reggie Jackson and Thomas for 20th all-time, now with 1,706.
Ramirez managed to rack up five RBIs despite missing out on a chance in the third when he struck out swinging on three pitches with the bases loaded.
"He's been doing it his whole career," Billingsley said of Ramirez. "One swing of the bat and you can change the game, the momentum. He's just such a dangerous hitter."
Billingsley (14-10) took care of the rest, tossing 6 1/3 shutout innings to beat one of Arizona's aces for the second straight week.
He gave up four hits and walked just one while striking out nine in his 11th consecutive start yielding three runs or fewer, a time in which he has gone 6-2 with a 2.48 ERA.
"From my experience in the Minor Leagues all the way up to here, he wants the ball in big-game situations and in big games," catcher Russell Martin said. "He's that type of guy, he's got that mentality."
Billingsley said he felt "fresh" after having six days of rest since his Aug. 30 start against Haren in Arizona, saying he has not gotten that much rest in a long time. He stayed aggressive with his fastball and threw his breaking ball for strikes to keep the D-backs' offense at bay, with its only rally coming in the seventh, when Billingsley loaded the bases only for Cory Wade to induce an inning-ending double play.
Torre compared Billingsley to former Yankees standout Andy Pettitte, a pitcher who enjoyed anonymity but also stepped up his performance in big games.
"Pettitte enjoyed the fact that writers would always talk to somebody else," Torre said, "but when the game was in the balance he wanted to be the guy who was going to pitch an important game, and that's what I see in Chad Billingsley."
Billingsley followed Derek Lowe's eight shutout innings on Friday night, extending Los Angeles' scoreless inning streak against Arizona to 19 before Scott Elbert allowed a pair of runs in the ninth with the game decided.
Before that inning, Dodgers pitchers had compiled a 0.77 ERA in their past four games against the D-backs, all wins for Los Angeles.
"It's crazy," Torre said. "They have an arsenal, they can put some points on the board, but it also speaks to the fact that pitching will stop hitting. It doesn't matter how good your hitters are."
The Dodgers' win delivered a mental blow by beating Arizona's duo of Webb and Haren on consecutive days for the second weekend in a row. The D-backs have lost back-to-back games started by Webb and Haren three straight turns through the rotation after they had lost consecutive Webb and Haren starts only twice all season before this drought.
Martin and Andre Ethier pushed the issue Saturday against Webb (19-7) by drawing three walks apiece on an afternoon in which Webb gave up seven runs on five hits and the six walks in 5 2/3 innings. Ethier walked in front of Ramirez's three-run homer and both Ethier and Martin walked with two outs in advance of his two-run double.
"We faced two pitchers that will make you swing out of the zone, but we took some tough pitches," Torre said.
Now that the streaky Dodgers have followed their eight straight losses with seven consecutive wins, four coming against their chief rivals' top guns, they can finally check the morning paper and see their team in the top column of the National League West, an unthinkable position a mere week ago.
"It just shows that we can turn it around," Martin said. "You're going to go through ups and downs during a season. You never want to lose eight in a row, but it's how you get up after you fall, and we've gotten up, and we've just got to keep doing what we've been doing lately."