A seven-time winner of the ATP 1000 event in Rome, Nadal is a heavy favourite to add to that tally this week, having already collected the Monte Carlo, Barcelona and Madrid titles in a stunning - and ominous - build-up to next month's French Open.
Dominic Thiem awaits in the last eight, but the in-form Austrian has had no answer of late to Nadal, who dispatched the world number seven in the final in both Barcelona and Madrid.
Should he progress to the last four, Nadal must deal with the more daunting prospect of Novak Djokovic or Juan Martin del Potro to earn a spot in the decider and stay on track for a potential sweep of 2017's major clay prizes.
After a routine hold to open the match, Nadal made a statement of intent by breaking Sock to love, working over the American's backhand to good effect.
With the injured Nick Kyrgios and the great Rod Laver watching from the stands, Nadal did brilliantly to react to a net cord and fend off break point.
He then held to go 3-0 up after the best rally of the set, somehow digging out a remarkable cross-court forehand and showing no signs of the physical problems that have impeded him in recent years.
The opening set stayed on serve after that, Sock showing better composure but proving unable to cope with Nadal's superior control of forehand depth and power.
The two men traded breaks in the first two games of the second set and Nadal was in trouble again at 2-1 and 0-30 down in the fourth, but a smoking forehand winner, down the line and on the run, proved the spark for an important hold.
It then stayed on serve until the ninth game, when the world number four upped the ante decisively.
Sock had no answer to a sudden flurry of heavier forehands, repeatedly burying shots into the net and then earning a code violation for his response upon dropping serve to love.
Nadal then duly held to love on his own serve to seal the contest with his first match point.