David Ferrer gave them a winning start against Sam Querrey and Nicolas Almagro battled to a five-set win against John Isner.
The Spanish are now overwhelming favourites to set up a final against either Argentina or the Czech Republic, who are locked at 1-1 in their semi-final after wins for Juan Martin Del Potro and Tomas Berdych.
Querrey took the opening set against all expectations against the US Open semi-finalist.
Ferrer is among the world's very best on clay and the world number five soon began to show his pedigree, cutting down on the error count which had been uncharacteristically high early on.
Once the 30-year-old levelled the contest, it seemed inevitable Querrey would bow to Ferrer in four sets. Despite having as many as nine break points in the fourth set, Querrey failed to convert.
In three minutes over three hours, Ferrer finished up a 4-6 6-2 6-2 6-4 winner over a man still battling back to where he wants to be in the world rankings after an injury-ruined 2011 season.
One-time world number 17 Querrey is knocking on the door of the top 20 again but a lack of clay-court expertise was his undoing.
Ferrer told Davis Cup Radio: "Sam is a very great player, it was a very close match but my performance was good.
"In the first set he was more aggressive than me, the second I broke in the first game and it was more easy."
Almagro had to battle for four hours and 16 minutes before finally seeing off Isner 6-4 4-6 6-4 3-6 7-5.
Almagro, leading by two sets to one, had six break points against the Isner serve early in the fourth set but could not capitalise.
And they went to a decider when Isner broke Almagro in the eighth game and held easily.
Isner saved three break points in the 10th game but could not hold out next time around, when a volley into the net handed Almagro a fourth match point which he took when Isner sent a forehand long.
Last year Spain saw off the United States in a quarter-final staged on hard courts in Houston and the reigning champions are hot favourites again to win the tie - even without talisman Rafael Nadal.
That is even more the case when you consider their 37-0 record in ties in which they have led 2-0, while the USA are 1-37 from 2-0 down.
In the other tie, Del Potro put Argentina 1-0 ahead against the Czech Republic with a convincing win over Radek Stepanek, the 2009 US Open champion prevailing 6-4 6-4 6-2.
Del Potro let two break points slip away in the seventh game but broke through on his next opportunity and closed the set out.
Stepanek broke early in the second but Del Potro levelled and broke for a second time, before breaking twice more to win the third set.
Del Potro, who has been suffering with a wrist injury, said: "It's difficult to play when you have some pain (wrist) but here in my country with a fantastic crowd, it's amazing for me and I really enjoyed it.
"I'm very passionate for all my competitions. I'm trying to play well and give a good show for the crowd - I have all my family, my parents and my friends close, it's great to show my tennis to them.
"I played really well, took my chances to break his serve. Sometimes with this crowd it gets easier than we expect but it's still a difficult match for Argentina."
Tomas Berdych levelled the tie at 1-1 after a thrilling match against Juan Monaco.
The Argentinian looked set to romp to victory when he led 1-6 6-4 6-1 4-1, but Berdych won nine straight games for a 4-0 lead in the deciding set.
Back came Monaco, winning four of the next five to get back on serve, but he was broken in the next game as Berdych sealed a 6-1 4-6 1-6 6-4 6-4 triumph.