As the four World Group ties got underway, with France against the US, Czech Republic versus Serbia and Argentina hosting Croatia all even at 1-1, Almagro thumped Melzer 6-2 6-2 6-4 and Ferrer thrashed Haider-Maurer 6-1 6-3 6-1.
Those performances put the favourites in command on the clay in blustery Marina d'Or on the Spanish coast.
"That was possibly my best match in Davis Cup," Almagro said in an interview with Spanish television after giving Spain, missing talisman and world number two Rafael Nadal, a blistering start as they bid for a fourth title in five years.
"I knew that I was going to be nervous and I was tense at the start and so were the first three or four games," added the world number 12. "But I threw off the shackles and then the tennis started to flow."
Harrison was warned by the umpire after slamming his racket into the ground when he double-faulted in the second set but said he enjoyed his first live Davis Cup singles rubber.
"I had a lot of fun," said the 19-year-old. "It's a great experience to represent your country, playing in an environment where you're representing something greater than yourself. I loved it."
Radek Stepanek and Janko Tipsarevic then traded blows for more than five hours before Serb Tipsarevic saved two match points to level at 7-7 in the final set and went on to clinch a nail-biting 5-7 6-4 6-4 4-6 9-7 success.
The match ended in controversy as Stepanek refused to shake hands with Tipsarevic, who had to be restrained by team mates and later accused the Czech of making an obscene gesture.
"Stepanek not only refused to shake hands but he also showed me a middle finger and this is completely outrageous," Tipsarevic told Serbian TV.
"Never in my career has this happened to me and all I can say is that I am completely stunned by his behaviour," the world number eight added.
"I think I played one of the worst matches for my country in the Davis Cup but the important thing is that I won to put us back on level terms."
There was a classic Davis Cup party atmosphere at Parque Roca in Buenos Aires for David Nalbandian's opening singles against Croatia’s Marin Cilic as Argentina seek to make up for the disappointment of losing to Spain in the 2011 and 2008 finals.
However, Cilic stayed focused amid the drumming and raucous chanting in the 14,000 capacity arena to edge the former world number three 5-7 6-4 4-6 7-6 6-3 in a five-hour thriller on the clay court.
World number 10 Juan Martin Del Potro then put the hosts level with a 6-2 7-6 6-1 win over big-serving Ivo Karlovic despite suffering stomach pain and vomiting on Friday morning and needing medical attention for a nosebleed in the third set.
Clay kings Spain, who have won their last 22 home Davis Cup ties, appear far too strong for underdogs Austria despite the absence of Nadal and the doubles pair in the 2011 final of Fernando Verdasco and Feliciano Lopez.
French Open champion Nadal has opted not to play in the competition in an Olympic year, citing the packed calendar, and is carrying a knee injury aggravated last week in Miami.
Verdasco and Lopez have been replaced after disappointing doubles performances in last year's victorious campaign.
Almagro and Ferrer ensured Nadal will not be missed too much as they put Spain on the verge of a September semi-final against France or United States.
Ferrer said his match was much easier than he expected.
"He (Haider-Maurer) made a lot of mistakes and I was able to play my game without ever really getting into a rhythm," the world number five told Spanish TV.
"Let's hope we can wrap things up tomorrow (in the doubles) but it's going to be a tricky match."
Spain captain Alex Corretja said he may have to deploy Almagro or Ferrer to partner Marcel Granollers on Saturday as Marc Lopez was carrying a back injury.
In sunny and breezy conditions at the Monte Carlo Country Club, Isner conjured the shot of the day against Simon, a stunning backhand pass, to break the Frenchman for a fourth time before serving out the match to love.
"That was one of the crazier points I have won and to do it on such a big point," Isner said. "Essentially it was a match point. If I win that, I am able to serve for the match."
France have a tough challenge on Saturday to prevent the US taking a 2-1 lead into Sunday's reverse singles when Julien Benneteau and Michael Llodra take on the world's number one doubles pair Bob and Mike Bryan.