Marc Gasol lifted Memphis to a 110-108 overtime win over the San Antonio Spurs with a clutch jump shot at the buzzer.
Klay Thompson tallied 24 points on Saturday for the Warriors, who seized a commanding 3-0 lead in the best-of-seven first-round Western Conference playoff series.
CJ McCollum scored 32 points and Damian Lillard added 31 for the Blazers, who will try to stay alive with a win in game four on Monday.
"They had a lot of adrenaline but we were able to withstand their runs and get back in the game," said Curry. "I love these kind of moments. I have confidence in myself to make those shots."
Elsewhere Saturday, Marc Gasol lifted Memphis to a 110-108 overtime win over the San Antonio Spurs with a clutch jump shot at the buzzer that allowed the Grizzlies to level their playoff series at 2-2.
Golden State was without forward Kevin Durant (calf injury), guard Shaun Livingston (finger) and forward Matt Barnes (ankle).
Warriors coach Steve Kerr also did not attend the game because of illness. His was replaced by assistant coach Mike Brown.
After the final buzzer, Curry collected the game ball and said he planned to deliver it to Kerr.
"Our coach is going through a lot right now," Curry said. "He told us to go out and 'win one for the Gipper.'"
Lillard scored 22 points and McCollum 17 as the Blazers went into halftime leading 67-54.
Curry and Thompson were a combined eight for 25 from the field at halftime.
In Memphis, Gasol's floater over Spurs defender LaMarcus Aldridge with 0.7 seconds left capped a thrilling back and forth first round playoff contest Saturday in front of a crowd of 18,100.
Kawhi Leonard scored a playoff career high 43 points for the Spurs, including San Antonio's final 16 points in the fourth quarter.
"Both teams played their hearts out," Spurs coach Gregg Popovich said. "Just a fantastic basketball game. The fans got their money's worth. Marc made a great shot. L.A. (Aldridge) contested it very well, it (went) down."
Leonard added eight rebounds, six steals and three assists. Leonard's fade-away jumper with 12 seconds left in regulation gave San Antonio a 96-94 lead.
But Leonard's brilliant performance was in vain as Mike Conley led Memphis with 35 points and had nine rebounds and eight assists.
Conley, who had 11 points in the final quarter, answered with a floater in the lane with four seconds left to tie the game at 96.
Leonard then missed a 21-footer at the buzzer to send the game into overtime.
Memphis won despite making a franchise postseason record 23 turnovers that led to 31 San Antonio points.
Elsewhere, DeMar DeRozan, held scoreless from the floor a game earlier, struck for 33 points and nine rebounds to lead Toronto over Milwaukee 87-76.
The visiting Raptors pulled level with Milwaukee at 2-2 in the best-of-seven Eastern Conference series, which continues Monday in Toronto.
In Atlanta, the Atlanta Hawks led wire-to-wire en route to a dominating 116-98 victory over Washington, cutting the Wizards lead in the playoff series to 2-1.
Forward Paul Millsap registered his second consecutive double-double by finishing with 29 points and 14 rebounds as the Hawks clawed their way back into the Eastern Conference series.
Millsap was 12 of 20 from the floor and had five assists. The only blemish on his night was missing four-of-nine free throws.
Game four of the series is Monday in Atlanta.
After the game, Millsap and Washington's Markieff Morris continued to fire verbal jabs at each other.
Morris called Millsap a "crybaby".
"He's a crybaby. You get all the calls when you're a crybaby. That's how I look at it," Morris said.
Millsap added: "It definitely got personal now, yes."
Atlanta also got 27 points and nine assists from Dennis Schroder. Rookie Taurean Prince scored 16 points.