Aranburu soloed in for the win ahead of a much-reduced bunch of favourites, with Omar Fraile (Astana-Premier Tech) winning the bunch sprint for second in front of Tadej Pogacar (UAE Team Emirates).
Aranburu embraced his teammate and fellow Basque rider Omar Fraile after the finish - Aranburu from the neighbouring Gipuzkoa province and Fraile from close to Bilbao himself. The pair had executed a top-class plan of attacking and then covering other moves enroute to a WorldTour victory, the first for the team in 2021.
After finishing tenth on the opening day's time trial, it looked as if the Astana rider would take the overall lead and the stage win. However, he struggled slightly on the last punchy rise into Sestao city centre, and Primoz Roglič (Jumbo-Visma) will retain his overall lead five seconds ahead of Aranburu with Brandon McNulty a further second behind.
"We agreed to take turns trying and after Omar went for it and they brought him back, it was my turn next," said Aranburu. "I could get a small gap, but then it rose a little further and I began to feel more certain of my chances.
"We knew there would be some important moves in the final climb, but that descent was also crucial.
"Winning at home, in La Itzulia (Tour of the Basque Country), is very special. The team's had good results this season, and I started out well, but this is the first victory. and that's always great."
Aranburu's Astana team has a number of leaders, including defending champion Ion Izagirre and Jakob Fuglsang, but for the present he sits highest on the general classification with Fraile also within the top ten.
"We have several strong leaders who could do that," said Aranburu of making a bid for the overall race win. "However, I felt good yesterday in the time trial and I also felt good today."
The rain fell heavily along the 154.8km route from Zalla to Sestao that culminated in the action on the late climb of La Asturiana (7.4 kilometres at 6.5 per cent).
Pogačar and David Gaudu (Groupama-FDJ) used the steep slopes at the bottom of the climb to start the attacks, jumping clear of the other contenders for stage and overall honours. Richard Carapaz (Ineos Grenadiers) crashed on a tight corner, and eventually, a Michael Woods-led peloton caught back up with the two escapees.
Pogačar was then watching the attacks from behind when his teammate Brandon McNulty, second overall, joined Roglič and Sergio Higuita (EF Education-Nippo) as they jumped across to an attack from Max Schachmann (Bora-Hansgrohe) towards the top.
They were caught just over the top of the climb as the course levelled off to a plateau, at which point Astana launched their 1-2 moves. Fraile's initial assault was neutralised by Wilco Kelderman (BORA-Hansgrohe) but there was no answer when Aranburu attacked immediately after.