Spain had put themselves within a point of a fourth final in five years when David Ferrer and Nicolas Almagro beat Sam Querrey and John Isner in Friday's singles but Granollers and Lopez were unable to close out the tie against the hugely experienced twins.
No slouches in doubles themselves having reached the last four of this month's US Open together, the Spanish pair were hampered by a calf injury to Granollers that required heavy strapping early in the second set.
Clearly hindered in his movement on the clay in Gijon, Granollers managed to save the Bryans' first match point with a fine drop volley but Lopez double faulted on the next, prompting the trademark chest-bump victory celebration from the US pair.
"We stayed the course the whole way and three hours 40 minutes was maybe one of the longest Davis Cup matches we ever played," Bob Bryan said.
"We're happy to get the team to Sunday and I have all the faith in John and Sam to play some good tennis tomorrow and we'll see what happens," added the 34-year-old, who with his brother is undefeated on clay in Davis Cup doubles.
Spain captain Alex Corretja said Granollers had initially told him he could not continue before changing his mind and battling on.
"We knew it was going to be very tough but we didn't expect the injury setback as well," Corretja said.
"The situation we were in was not easy but in the end the Bryan brothers have a lot of experience, and although they were troubled at times they knew how to play to their strengths."
Ferrer can put Spain 3-1 ahead and clinch a place in November's final with a win against Isner in Sunday's opening reverse singles, with Almagro due to play Querrey afterwards.
Granollers and Lopez missed out on a chance to meet the Bryans in the US Open final when Lopez was forced out of their semi against Leander Paes and Radek Stepanek with a calf injury and the twins went on to win a 12th Grand Slam doubles title.
Bob Bryan said they had thought that this time it would be Granollers who would have to retire.
"At times we thought he was going to quit but he kept getting the balls and hitting the serves," he said.
Mike added: "We've played over here before and the Spanish fans are great.
"They were pulling for these guys, who are heroes for Spain, but you know we're happy to silence them a little bit."
Spain - firm favourites to win a fourth title in five years despite Rafael Nadal's injury - are on a 23-tie unbeaten run at home, a World Group record that dates back to 1999 when they lost 3-2 to Brazil in Lerida with current captain Alex Corretja in the side.
The semi-final in the northern Spanish city pits the US, the most successful Davis Cup nation with 32 titles, against the country that has dominated the competition over the past decade, with four titles since their first one in 2000.