Victory in San Sebastian came via first-half goals from Justin Kluivert and Rayan as the travelling Cherries were in dreamland at the break.
Sergio Gomez's goal forced Marco Rose's team to dig in late on, but the away fans were able to celebrate an unforgettable night far removed from their threat of financial administration just over a decade ago.
England international Alex Scott was linked with a move away from the club over the summer, as Bournemouth declined several transfer offers on him, and Rose's No.8 believes there can be more history for the team in the coming months.
"t was tough out there. First half, I think we were brilliant. We really took the game to them.
"We started quickly, as we always do, and then the second half was a lot tougher. Their fans got behind them, it was loud and they really pressed us.
"I think we did well in the end, secured the win, and yeah, I'm sure the fans are really happy.
"It's enjoyable. It's still like that in the Premier League, when I get to play that every week. You still get that buzz and that feeling.
"It's a new competition for me and for the club and a lot of the lads. We're grateful to be here. We really want to push and do something special in this competition."
Next up for Bournemouth is a home PL clash with Liverpool on September 20th and their next European date is at home to Sturm Graz on October 15th.