Alcarath had started his campaign in this session with a quick win over Japanese Yoshihito Nishioka 6-4 6-4 in an hour and 15 minutes on Wednesday.
And Alkarath will meet the Russian Andrei Rublev or the young Danish Holger Ronh in the next round.
Alcarath finished the first set 6-1 very easily, but the Bulgarian found his balance in the second and advanced 3-1, breaking the Spaniard, but the latter responded strongly by winning the next five games and sealing the match in his favour.
After the win, Alcarath said: “He wasn’t my opponent in his day, he didn’t do his best, but I put on a good show.”