Nico Hoerner had three hits and scored three times, helping Chicago close out a 5-2 road trip. Jeimer Candelario homered and drove in three runs.
The Cubs (69-61) took three of four in Pittsburgh. Next up is a big three-game series against NL Central-leading Milwaukee at Wrigley Field beginning on Monday night.
Bellinger singled in Hoerner in the first inning. He doubled home two more runs in the fifth, giving Chicago a 5-1 lead. The 2019 NL MVP added another two-run double in the ninth and scored the Cubs' final run on Yan Gomes' groundout.
Bellinger has 16 RBIs in his last nine games and a MLB-best 53 RBIs since July 1. He has reached safely in 34 of his last 38 games.
Joshua Palacios had two of Pittsburgh's four hits. Bailey Falter (1-8) was tagged for six runs and seven hits in 4 2/3 innings.
The Pirates have lost nine of 10 against the Cubs this year.
Candelario put Chicago ahead to stay with his 19th homer, a tiebreaking two-run shot in the fourth. He also drove in a run with a fielder's choice in the eighth.
Cubs right-hander Javier Assad (3-2) struck out seven in seven innings. He surrendered three hits and walked two.
Seiya Suzuki had two hits and scored two runs for Chicago, extending his hitting streak to a career-best 10 games.
The Pirates recalled right-hander Cody Bolton from Triple-A Indianapolis. Right-hander Osvaldo Bido was optioned to Triple-A. Bolton allowed one hit in 2 1/3 scoreless innings in the loss.
Cubs: RHP Jameson Taillon (7-8, 5.60 ERA) is scheduled to start Monday against LHP Wade Miley (6-3, 3.18 ERA) and Milwaukee.
Pirates: RHP Johan Oviedo (7-13, 4.46) starts for Pittsburgh in Monday's series opener at Kansas City.