Looking in peak condition and every inch a potential champion, Murray hardly broke sweat as he took his Slovakian opponent to pieces in an hour and 24 minutes, winning 6-1 6-1 6-0.
"Getting games finished quickly helps. I feel like that cost me a little bit at the French Open," said Murray after the quickfire victory.
"Not that I would necessarily have beaten Rafa, but I played a lot of sets and in a lot of those sets, I was up. If you can finish matches as quickly as possible, it helps."
Rola did earn three break points during the match, but was unable to take any of those chances.
And Murray was utterly ruthless, particularly on Rola's second serve: the defending champion won 71% of the points when Rola failed to find the box with his first serves.
While the British number one was winning Wimbledon last year, Rola was winding up a successful college tennis career for Ohio State University. The contrast in quality was stark.
Some of the biggest cheers on an otherwise partisan Court One were reserved for Rola's two winning games, the crowd willing him to avoid further embarrassment.
But Murray, blasting winners from both sides of the court, put the 23-year-old firmly in his place to set up a third round clash with either Czech Jan Hernych or Spain's Roberto Bautista.
"I played well today," Murray told the BBC after his 16th consecutive singles victory at the All England Club (seven at the 2012 Olympics, seven at last year's Wimbledon and now two this year).
But he cautioned against reading too much into the one-sided match, pointing out that his opponent was out of his element.
"This is the first year he's played on grass. He's just come out of college and broken into the top 100.
"It was tough for him, because he doesn't have a lot of grass-court experience, but he'll definitely keep improving. I had to concentrate on my side of the net today, though."
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