Murray, the third seed, coasted to a 6-1, 6-1, 6-0 mauling of 23-year-old Rola who was playing just the 10th match of his career having only graduated from university in Ohio last year.
The British star eased to victory in just 84 minutes, hitting seven aces and 27 winners against the world number 92 and goes on to face either Jan Hernych of the Czech Republic or Spanish 27th seed Roberto Bautista Agut for a place in the last 16.
"I took care of my serve for the majority of the match and I played well. If you can finish matches as quick as possible then that's better in the long run."
French Open semi-finalist Ernests Gulbis became the highest ranked man to lose so far when the 12th seed went down to Sergiy Stakhovsky of the Ukraine, 6-4, 6-3, 7-6 (7/5).
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Stakhovksy, who shocked Roger Federer in the second round in 2013, next faces either France's Jeremy Chardy or Australia's Marinko Matosevic.
"I went to play blackjack, but there was no word how much I won or how much I lost. They (reporters) asked me how much I lost. I said, A lot. I was joking," he said.
"Next day in Latvia they say I lost all my winnings. My mother sends me a message next day asking am I crazy. I may be but I'm not stupid."
Australian Open champion Li Na, a three-time quarter-finalist at the All England Club, swept to a 6-2, 6-2 victory over Austria's Yvonne Meusburger, hitting 33 winners to just four from the world number 38.
She said she was unconcerned about her 21 unforced errors.
"If you want to play more aggressive, this is the normal way," she explained.
Five-time champion Williams, 34, and playing in her 17th Wimbledon, defeated pint-sized Japanese Kurumi Nara 7-6 (7/4), 6-1 in a battle of little and large on Court 3.