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.
Thompson and Green hit back-to-back three-pointers to give the Warriors a 95-87 lead with 6:25 remaining. Green made another three-pointer and hit a layup to extend the lead to 103-90 with 3:11 left.
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. Harrison Barnes and Marreese Speights added 11 points apiece for the Warriors, who shot 12 of 30 from three-point range and had 28 fast-break points to the Bulls' 13.
Philadelphia 108, at Detroit 101 (OT): Hollis Thompson's three-pointer in the final seconds for the 76ers sent the game to overtime. The Pistons managed just one point in the extra time in this matchup of the teams with the NBA's two worst records. It took almost half the overtime for either team to score. Kentavious Caldwell-Pope finally made a free throw for Detroit with 2:37 left, but the 76ers scored the game's final eight points.
at Houston 100, Phoenix 95: Trevor Ariza and Pat Beverley scored 19 points apiece to lead the Rockets to their fourth straight victory. Houston won for the seventh time in the nine games All-Star center Dwight Howard (knee strain) has missed. The Rockets never trailed and led by as many as 22 points.
at San Antonio 123, Minnesota 101: The Spurs had a season-high 30 assists and seven players in double figures, led by Marco Belinelli with 20 points and 18 points each from Kawhi Leonard and Cory Joseph. The Timberwolves have lost five straight.