'(Almagro) has a very big serve,' Murray said.
'He served well in the first set. After the rain interruption, I didn't change much in my game. I was just getting more accustomed to the fast court. I only had an hour of training on Tuesday.'
Murray described looming opponent Stepanek as 'a tricky player.'
Nadal, competing in his second event since returning from two months of rest for his damaged knees, was facing Italian Andreas Seppi in the second round after a bye.
Seventh seed Jo-Wilfried Tsonga, who defeated Federer five days ago in the Montreal quarter-finals, was dispatched under a barrage of 20 aces by Aussie qualifier Chris Guccione.
Fourth seed Novak Djokovic, last year's losing finalist to Andy Murray, beat Croatian veteran Ivan Ljubicic 7-6 (7-5), 6-4.
France's Paul-Henri Mathieu beat Croatian Ivo Karlovic 7-6 (11-9), 6-4 to eliminate one of the biggest servers in the game at the second-round stage.
Czech Tomas Berdych beat Germany's Philipp Petzschner 7-6 (10-8), 6-7 (7-9), 6-4 in more than two and a half hours.