Top seed Alcaraz defeated American Michelsen 7–6(1), 4–6, 6–1 to reach the second round of the ATP 500 tournament.
The Spaniard had to save three set points in a tense opening set before dominating the tie-break. Michelsen responded by breaking Alcaraz twice in the second set and eventually levelled the match.
Alcaraz then regained control in the deciding set, racing into a 2–0 lead before completing the victory.
The seven-time Grand Slam champion has been adapting to a modified service motion and admitted that Tokyo's rain-affected preparation and slower outdoor conditions made the transition difficult.
Alcaraz will face Italy's Matteo Arnaldi in the second round.
Third seed Fritz suffered one of the biggest shocks of the day, losing 6–7(7), 6–4, 6–3 to Spanish qualifier Jaume Munar.
Fritz, who won the Japan Open in 2022 and reached the final in 2025, was unable to close out the match after taking the opening set in a tight tie-break. Munar, ranked 64th in the world, secured his third victory of the season against a top-20 opponent.
Sixth seed Ruud also departed in the opening round after Luciano Darderi defeated the Norwegian 7–6(3), 6–3.
Darderi produced a strong serving display, winning 87 per cent of points behind his first serve and hitting 13 aces. The Italian will next face Kyrian Jacquet.
Seventh seed Tommy Paul was beaten 6–1, 6–2 by Alejandro Tabilo, while former world No. 4 Holger Rune's comeback suffered another setback as Kyrian Jacquet defeated him 6–3, 6–1.
The Japan Open is being played at Ariake Colosseum from September 28 to October 6, with the main draw featuring 32 singles players.
• Carlos Alcaraz: defeated Alex Michelsen 7–6(1), 4–6, 6–1
• Jaume Munar: defeated Taylor Fritz 6–7(7), 6–4, 6–3
• Luciano Darderi: defeated Casper Ruud 7–6(3), 6–3
• Alejandro Tabilo: defeated Tommy Paul 6–1, 6–2
• Kyrian Jacquet: defeated Holger Rune 6–3, 6–1
• Alcaraz's next opponent: Matteo Arnaldi
• Tournament: Kinoshita Group Japan Open, ATP 500
• Venue: Ariake Colosseum, Tokyo