Defending champion Alcaraz overcomes wobble to win Queen's opener
Spain's Alcaraz, who lifted his third Grand Slam at the French Open earlier this month, was not at his best in his first grass-court match of 2024 but recovered from a mid-match dip to triumph.
The top seed committed just one unforced error in the first set to take a grip on the contest but his level dipped at the start of the second set and he trailed 2-5.
From there he battled back impressively, saving three set points on serve at 4-5 before sealing victory to extend his winning streak on grass to 13 matches.
The world number two, who followed up last year's victory at Queen's by winning his first Wimbledon, will next face Stuttgart champion Jack Draper or Argentine Mariano Navone.
Earlier, Lorenzo Musetti upset Australia's De Minaur, ranked seventh in the world, 1-6, 6-4, 6-2.
De Minaur came to the tournament fresh from winning the 's-Hertogenbosch grass-court event in the Netherlands at the weekend.
There were also wins for former Wimbledon quarter-finalist Taylor Fritz and fellow Americans Tommy Paul and Sebastian Korda. Italian Matteo Arnaldi eliminated eighth seed Ugo Humbert.