Ramirez got things going early with a two-run home run in the first inning off Ryan Dempster, his first homer of the spring.
Playing defense for the first time this spring, Ramirez then took an extra-base hit away from Tyler Colvin in the fourth inning with a running catch at the base of the left field wall.
"Manny can catch the ball; if he gets near it he's going to catch it," manager Joe Torre said. "And he got three hits in his last game in Taiwan (on Sunday). Timing-wise he's fine. He's hitting line drives and is much more balanced than he was last year."
Billingsley was an All-Star for the first time last year but struggled in the second half. He has dedicated his spring to correcting a flaw in his delivery.
"Everything felt good out there today," Billingsley said. "I'm just kind of fine-tuning things. Today the fastball felt good. I still have some work to do but it felt good and overall I'm happy with it."
Despite giving up the home run to Ramirez, Dempster said the outing was exactly what he was looking for with Opening Day just over two weeks away.
"(Ramirez) did what he was supposed to with a middle-in fastball," Dempster said. "It doesn't change my approach. He's a real good hitter. He's hit a few before and he'll hit some more. I've given up my share of them."
Thursday's crowd of 13,391 at Camelback Ranch set a single-game Cactus League record. The Cubs have drawn nine of the top 10 single-game crowds in league history. ... Torre is letting his pitchers come to the plate for the first time this spring. Billingsley went 0 for 1. ... Dodgers reliever Hong-Chih Kuo, who hasn't pitched in a week because of elbow soreness, is scheduled to take the mound Friday. ... The Cubs' Aramis Ramirez was a scratch from Thursday's game with a sore triceps. ... Cubs LHP Ted Lilly, who had arthroscopic surgery on his shoulder in the offseason, threw to hitters for the first time Thursday and is targeting a mid-April return to the rotation.