Murray had won his last four meetings against Granollers and only lost twice in nine, but the emphatic score-line was harsh on the world number 45, who was particularly threatening at the end of the first set.
Two games, lasting 23 minutes, had Murray scrambling but the Scot survived and never looked back thereafter.
"It was tough obviously, had it gone to 5-5 then the first set becomes a really tough one and all the pressure is on me at the end of that set," Murray said. "Thankfully I got through that 5-4 game and the momentum was back with me."