The 20-year-old, who claimed his second grand slam title on Sunday by beating 23-time major champion Novak Djokovic on the All England Club lawns, did not enjoy the smoothest shift back to clay in Nice, France, on his debut in the mixed team event.
Taking to the court after Elise Mertens beat Rebeka Masarova 7-6(7-3) 2-6 (10-5) to put Belgium 1-0 ahead, Alcaraz dropped his serve twice in sweltering conditions to surrender the opening set tamely to his seasoned opponent.
World No.111 Goffin, who defeated Alcaraz the last time they played after the youngster bagged the 2022 US Open crown, broke in the opening game of the next set and consolidated his lead to heap the pressure on his opponent.
Alcaraz responded by clawing back to 3-3 and rode his luck after both players wobbled on serve to level the match at a set apiece before switching on the after-burners from 0-4 down in the wildly swinging super tiebreak to wrap up the victory.
Alcaraz and Masarova, who replaced the injured Paula Badosa in the squad, will face Goffin and Mertens in the mixed doubles rubber later.
Spain take on Croatia on Saturday.
In Friday's other tie, France and Switzerland were locked at 1-1 as Alize Cornet downed Celine Naef 1-6 6-3 (10-8) before Richard Gasquet slumped to a 3-6 6-3 (10-8) defeat by Leandro Riedi to set up a deciding mixed doubles match.
The winner will reach Sunday's final after both teams beat a Denmark side featuring men's world number six Holger Rune.
The relaunched Hopman Cup has returned to the tennis calendar this week after a four-year absence, having lost its spot ahead of the Australian Open as a result of the short-lived ATP Cup men's team event.
The last edition of the Hopman Cup, which began in 1989 and was named after Australian great Harry Hopman, saw Roger Federer lead Switzerland to the title against Germany.Â
