The Blazers, playing the second half of a back to back, appeared to be tiring late in the third quarter when things got chippy between the teams not long after Matthews was whistled for a technical foul when Aldridge was knocked flat on his back.
Moments later, Portland reserve center Joel Freeland and Golden State's Andrew Bogut then got into a shoving match in front of the Warriors bench.
Aldridge joined the fray, which quickly escalated. At one point, Matthews was stopped after charging toward a group of Golden State players, while Warriors reserve Draymond Green had to be restrained by several teammates and coaches.
Referees conferred for several minutes and watched replays on a monitor before issuing six technical fouls and three ejections. Matthews and teammate Mo Williams, along with Green, were all tossed.
Golden State, which led 77-63 at the time, couldn't hold on.
Portland pulled within 84-81 heading into the fourth then went on a 12-2 run to take the lead for good.
Aldridge, who missed six of his first seven shots, scored 15 points over the final 12 minutes while going 11 of 14 from the free throw line.
That was enough to propel the Blazers to their second come-from-behind win in as many nights.
Not even the return of Stephen Curry could prevent Golden State from letting this one get away.
Curry, who had 22 points and 11 assists, returned to the Warriors lineup after missing two games with a concussion. Golden State was still short-handed, however, as Iguodala sat out with a strained left hamstring suffered in Friday's loss to the Los Angeles Lakers.
The Blazers got off to another cold start before storming back.
One night after rallying from 21 down to beat the Chicago Bulls 98-95, Portland again had to play from behind.
Thompson scored 18 points in the first half and Golden State led 59-47 midway through the second quarter while taking advantage of Lillard's slow start.
Lillard, who grew up about 10 minutes from Oracle Arena, missed his first six shots and didn't score until 10:21 remained in the first half.
Aldridge also struggled with his shot early, but had six points over the final three minutes to help trim the Warriors' halftime lead to 54-49.
Curry made back-to-back 3s in the third quarter and Golden State upped its lead to 77-63 before emotions bubbled over.
Notes: The Warriors are 5-2 at home this season ... Seattle Seahawks running back Marshawn Lynch and professional poker player Phil Hellmuth were among those in attendance at courtside.