The gunners rode their luck after surviving a second-half barrage from the Blades at Bramall Lane.
Nicolas Pepe put Arsenal ahead with a first-half penalty after Chris Basham fouled Alexandre Lacazette.
David McGoldrick equalised with three minutes left, but on-loan Real Madrid midfielder Ceballos settled a hard-fought quarter-final in the final moments.
Arsenal join Manchester United in the last four, with Leicester facing Chelsea and Newcastle hosting Manchester City in Sunday’s other quarter-finals.
Arteta was Arsenal’s captain when they won the FA Cup final against Hull in 2014.
And the Gunners boss remains on course to get his hands on the silverware again as Arsenal look to win the competition for the 14th time.
After losing their first two matches following the restart, Arsenal, who beat Southampton in the Premier League in midweek, have now won two in a row.
The Blades have gone winless in their four matches since the English season restarted, ruining their hopes of a push to qualify for the Champions League and ending their FA Cup campaign.
Arteta made five changes, with Pierre-Emerick Aubameyang and Eddie Nketiah among those left out.
There was no place for Matteo Guendouzi again after the Arsenal midfielder’s role in the brawl against Brighton, while Mesut Ozil was also absent from the Gunners squad.
David Luiz was back in Arsenal’s defence after serving a suspension for the red card he picked up during a disastrous substitute appearance in the defeat at Manchester City last week.
It wasn’t long before Arsenal’s defensive frailties were on display when John Lundstram nodded home from Oli McBurnie’s header, but the goal was ruled out by VAR for offside against the Blades midfielder.
Despite their unconvincing start, Arsenal grabbed the lead in the 25th minute.