Saturday’s victory was the fifth straight for the Clippers, who were led by big man Blake Griffin's double-double and Jamal Crawford's prolific shooting to improve to 7-2.
Griffin scored a game high 26 points and added 10 rebounds while Crawford chimed in with 22 points of his own as the home side dominated.
"It's about my team-mates, it's about how they space the floor and are giving me the confidence throughout the game," Griffin told reporters.
"It was a very important win."
Having played eight of their opening nine games at home the Clippers must now prove their worth on the road as they head for a tough four-game run in five days, including contests against the San Antonio Spurs (8-2) and Oklahoma City Thunder (7-3).
The only other time in franchise history the Clippers won seven of their opening nine games was 2005-06 where they finished 47-35 on the year, and ended up one victory short of the Western Conference Finals.
"Yeah, we're thrilled. But it's early," head coach Vinny Del Negro said.
"We're happy but we let a couple of games slip away.
"Against some of the top teams I felt we played solid basketball at times but we have to be more consistent.
"It's early on and guys are still getting their feet under them a little bit.
"We have a tough road trip coming up and we have to handle it right. We'll see where we are after that; it will be a good test for us."
The Bulls, still playing without injured former league MVP Derrick Rose, trailed for the majority of the night and dropped to 5-4 on the season.
Carlos Boozer was the pick of the Bulls line-up with 22 points and 12 assists.
