The third-seeded Almagro, who won here in 2006 and 2007, reeled off winners to break Andujar five times and easily advance to the second round on the indoor hard court.
Almagro said that he feels like he was rediscovered his winning form.
"I have been playing well now after a period when I was a little lost and didn't really know what to do," Almagro said. "Thanks to the people supporting me I have found my way forward again. I feel strong, but I just need to focus on going match by match."
Two favorites of the home crowd, Fernando Verdasco and Feliciano Lopez, both lost in straight sets. Qualifier Michal Przysiezny ousted Verdasco 6-3, 7-6 (1) after Julien Benneteau thrashed Lopez 6-3, 6-1.
World No. 3 and reigning champion David Ferrer debuts on Wednesday against Gael Monfils, while John Isner plays Ernests Gulbis and second-seeded Tommy Haas faces Philipp Kohlschreiber in an all-German match.