The World No. 12 eased past 2019 Rolex Monte-Carlo Masters finalist Lajovic 6-4 6-3 to win his 14th consecutive match. Ruud has won his past three tournaments (Bastad, Gstaad and Kitzbuhel), and his record in 2021 now stands at 37-9.
There were no breaks in the opening set until the final game, when Lajovic hit four unforced errors to donate the break to Ruud. The Norwiegen had no such trouble on serve in the opener, winning 20 of his 22 service points and 100 per cent of his second-serve points.
There was little to separate the two players in the second set, but it was the sixth seed who again gained a crucial break in the latter stages of his victory over the Serbian.
Ruud moves on to the quarter-finals of an ATP Tour event for the 11th time this season as he continues his pursuit of a first ATP Masters 1000 level title.
The 22-year-old will next play third seed Stefanos Tsitsipas in the quarter-finals. Ruud won their only previous ATP Head2Head meeting this year in Madrid.