The third-tier team from the Spanish island, known around the world for its lively nightlife, stunned the visiting side with an early goal from forward Javi Perez.
Ibiza looked to have doubled its lead soon after but Barcelona had referee Pablo Gonzalez Fuertes to thank for ruling it out.
The visiting side, which struggled to a 1-0 win over 10-man Granada in Quique Setien’s first game in charge on Sunday, was then left thanking the woodwork as Ibiza once again went close to extending its advantage.
Griezmann eventually silenced the 6,445-capacity Estadio Municipal de Can Misses — expanded from its usual 4,500 just for this game — with a goal in the 72nd minute, before sealing victory in the fourth minute of stoppage time.
“Griezmann avoids total ridicule,” wrote Diario AS of the labored victory. “A disastrous Barcelona takes advantage of the lack of VAR to eliminate in stoppage time an Ibiza team that stripped the blaugrana.”
Barcelona, winner of the Copa del Rey in four of the last five seasons, was without the rested Lionel Messi but still boasted a strong team featuring Griezmann, Frenkie de Jong and Ivan Rakitic.
Newspaper Sport was also damning in its criticism of Setien’s side, writing: “Griezmann saves Barca from a KO in the last minute. Ibiza dominated a club that didn’t find its game and had to resort again to individualities.”
The Barcelona boss was also critical of his team, telling reporters: “I didn’t like the team in the first half, but I understand the difficulties you encounter in matches such as this.
“Due to the artificial grass and against an intense and very aggressive team, which shut up very well.”
Setien met a familiar face in Pablo Alfaroin the opposition dugout, a former Barcelona player and teammate for three years at Racing Santander.
This may have been Ibiza’s first ever appearance in the Copa del Rey, but expect to see more of the island team in future.
The club is funded by wealthy president Amadeo Salvo, who has overseen two promotions in three seasons since the club reformed from UD Ibiza-Eivissa in 2015.