After taking the first set on a tie-break, the Spaniard dominated against the world number 85. Nadal will face Japan’s Taro Daniel or American Tommy Paul next.
“At the end of that first set it was important to get the break point back and I played a good point at 6-6, then hit a good winner to win the set.
Earlier this year, Lajovic broke eventual champion Roger Federer at the first opportunity in their second-round meeting at Wimbledon on his way to losing an opening-set tie-break and the match.
But his first-serve percentage (83%) and the rate of winners (nine) both dropped substantially over the next two as Nadal’s class showed.
Once again, the 27-year-old’s best work came early as he matched Nadal for much of the first set with an unexpectedly high standard of tennis.