An explosive 11th-year combo guard, Crawford joined the Blazers as a free agent before the season but has struggled to find his role in Portland.
"I envisioned more nights like this when I first came here, but everything happens for a reason and better late than never," Crawford said.
David Lee had 21 points and 14 rebounds for the Warriors (22-35), while Nate Robinson added 19 points and eight assists. Golden State trailed by as many as 15 in the third quarter but fought back to tie the game at 95.
Portland led 109-106 after Klay Thompson made a 3-pointer for the Warriors, but Matthews knocked down a midrange jumper and then a 3-pointer to put away the game.
An examination of Aldridge's hip done Tuesday in Vail, Colo., showed an "abnormality," according to interim general manager Chad Buchanan. That could cause Portland to shut him down for the rest of the season and effectively end its faint playoff hopes. The Blazers are 4½ games back of Denver for the eighth playoff spot in the West.
"Finally, we are playing with a sense of urgency," Matthews said. "I wish we could have done that two months ago."
Aldridge is averaging 21.7 points and 8.0 rebounds and was named to the All-Star team this season for the first time. Hickson, who has scored in double digits in eight of 12 games since Portland picked him up off waivers from Sacramento, replaced him in the starting lineup.
The Warriors were coming off a 123-84 loss to Denver on Monday. They have dropped 11 of 15 games since trading Monta Ellis in February and are out of the playoff race.
"That may be an excuse for other teams, but for us that's unacceptable," Golden State coach Mark Jackson said. "The last two games we haven't been ourselves."
Portland went up 56-48 in the second quarter after back-to-back 3-pointers from Nicolas Batum and Luke Babbitt. Portland was up 85-75 after the third quarter, but the Warriors opened up the fourth on a 10-0 run to tie the score. But they didn't get stops at the end, allowing Portland to tally its second-highest scoring total of the season.
"For the most part, our team played hard," Robinson said. "We just gave up a lot of baskets that were uncalled for."
Crawford has made 26 straight free throws. ... Batum returned after missing a game with tendinitis in his left quad. ... Adam Richman from the Food Network show "Man vs. Food" was in the crowd. ... Portland C Joel Przybilla had 14 rebounds, his most since April 11, 2009.