Cameron Norrie and Yosuke Watanuki will take on each other in the second round of the 2023 WTA Madrid Open on April 29.
The Italian blew a break lead in the second set, but held his nerve in the tie-break to earn his first ATP Masters 1000 victory.
Andy Murray and Andrea Vavassori will take on each other in the first round of the 2023 WTA Madrid Open on April 27.
Rune trailed 2-5, 40/15 on the Van de Zandschulp serve in the third set as he battled a problem with his upper right arm.
Carlos Alcaraz, the reigning champion, will be the overwhelming favourite to win in Madrid and will try to become just the second person to successfully defend his title.
Alcaraz defeated World No. 5 Tsitsipas in 79 minutes despite dropping serve in the third game of the match.
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.
The 19-year-old defeated Alejandro Davidovich Fokina 7-6(5), 6-4 on Friday to advance to the semi-finals at home after defeating Roberto Bautista Agut on Thursday.
Tsitsipas maintained control throughout the hour-and-twenty-one minute match at the clay-court ATP 500, dominating De Minaur.
The Greek returned all of the three break points and recorded win percentages of 85% and 50% on the first and second serves respectively.