Bilbao conceded an early goal following Oscar Trejo’s smart finish, however, Inaki levelled the score for the home side in the 14th minute.
Oihan Sancet then put Bilbao ahead for the first time at the half-hour mark before Nico made it 3-1 with another brilliant finish.
Radamel Falcao came off the bench to score for Vallecano, but his goal only counted as a consolation as the visitors fell to a 3-2 defeat.
The goals scored by Inaki and Nico, though, saw them become the first pair of brothers to score for the same team in the same La Liga match in the last 17 years.
The last duo to do that was Diego and Gabi Milito when they both scored for Real Zaragoza against Barcelona at Camp Nou in 2005.
Meanwhile, Inaki and Nico are set to join the growing list of brothers who played for different national teams.
Inaki recently switched nationality from Spain to Ghana and is set to make his international bow in the Black Stars’ friendlies in September against Brazil and Nicaragua.
Meanwhile, Nico has also earned his debut call-up to the Span national team ahead of their UEFA Nations League games against Switzerland and Portugal later this month.