The shot with 6:49 left in the half put Curry in front of Ray Allen's mark of 269 set in 2005-06.
He made 16 3-pointers in the previous two games to close within one of Allen's record set with the Seattle SuperSonics. Curry hit his first 3 of the night with 6:55 to go in the first quarter.
Golden State's bench jumped to cheer following the record-breaking shot, and a group of Warriors fans behind the team's bench at the Rose Garden gave Curry an extended standing ovation.
His dad, Dell Curry, was a teammate of Allen's in Milwaukee during the 1998-99 season -- when the elder Curry shot a career-best 47.6 percent from 3-point range while making 69 from beyond the arc.
The younger Curry and second-year shooting guard Klay Thompson went into the game with 474 combined 3-pointers, shattering the previous NBA record of 435 by Dennis Scott and Nick Anderson for the most by any tandem. Curry and Thompson added two apiece in the first half against the Blazers.
The Warriors drafted Curry seventh overall in 2009. After a sensational rookie season, Curry was hit by injuries, spending the past two summers recovering from surgery on his right ankle.
Healthy for most of this season, Curry came into the game against the Blazers averaging nearly 3.5 3-pointers.
He has been at his best this season in big games. He scored a career-high 54 points in a loss to the Knicks at Madison Square Garden on Feb. 27. He also had 47 points in a loss at the Lakers last Friday.
"The one thing I know about Steph Curry -- he's not afraid when the lights are brightest," Warriors coach Mark Jackson said.
Following the record-breaking shot, Jackson sat Curry for the rest of the half.