Elsewhere in Doha, Alex de Minaur claimed a 6-4 6-4 victory over Botic van de Zandschulp, his 200th tour-level hard-court win to set up a quarter-final against fifth seed Andrey Rublev, who beat Nuno Borges 6-3 6-4.
The 23-year-old broke serve in the first game and repeated the feat at 4-2, with O’Connell taking just one game in the second set to exit in 59 minutes.
At one stage the Italian clocked up six consecutive games to force a decider but Alcaraz ultimately saw it through in one hour and 53 minutes.
His quarter-final opponent will be Matteo Berrettini, who built on victory over Novak Djokovic on Tuesday to progress to the last-eight by beating Tallon Griekspoor 7-6 6-7 6-4 and is yet to have his serve broken so far in Doha.
The Italian was pushed hard by his opponent with the second set going to a tense tie-break from which the Dutchman emerged victorious before the unseeded Berrettini won through in the third.
