Klay Thompson added 24 points for the Warriors, who extended their league-best record to 17-2.
The Warriors improved to 10-1 on the road. They previously won a franchise-record 11 straight games from Dec. 29, 1971 to Jan. 22, 1972.
The Bulls fell to just 2-5 at home.
The Warriors had lost five straight and 11 of 12 in Chicago and were 6-28 over 35 years there.
Gasol tipped in a basket to cut the lead to 107-100 with 31.5 seconds left, but Stephen Curry went five of six at the free throw line in the final seconds.
Green's previous career high was 24 points against the Clippers on Nov. 5. He entered Saturday averaging 12.5 points.
Curry had 19 points to give him double-figure scoring in 18 of 19 games.
Philadelphia 108, at Detroit 101 (OT): Hollis Thompson's three-pointer in the final seconds for the 76ers sent the game to overtime. The
at Houston 100, Phoenix 95: