Despite only winning four games in their previous two encounters, the 32-year-old Lajovic prevailed 6-4, 7-6(6) after surviving 15 of 16 break points.
By the end of the previous year, Nadal had only participated in nine matches, and he was unable to start over in 2023.
Rublev advanced to his first ATP Masters 1000 quarterfinal since last May, when he reached the final eight in Madrid, with his 15th victory of the year.
On Court Rainier III, the second-seeded Tsitsipas defeated the World No. 58 Jarry in 93 minutes with a flawless performance.
The 21-year-old Italian won the match in two hours and 54 minutes by taking advantage of Djokovic's poor serving while playing in wet and windy conditions.
In the absence of Rafael Nadal and Carlos Alcaraz, the defending champion Stefanos Tsitsipas and the hot tandem of Daniil Medvedev and Jannik Sinner will attempt to challenge the W...
The Austrian won with confidence in the first round against fellow countryman Sebastian Ofner and followed it up with a commanding performance against Ben Shelton.
Since defeating Sinner in the Rotterdam final in February, Medvedev is now 6-0 against Sinner in their head to heads.
The World No. 1 kept the American at arm's length in a smooth 6-4, 6-2 victory in a Thursday night quarterfinal.
Khachanov had to dig deep to register a fantastic 7-6 (7-4), 6-4 win over the Greek, who failed to get into his stride against the Russian.