A last-gasp strike from Dani Ceballos capped a dramatic finale at Bramall Lane and propelled us into the semi-finals of the Emirates FA Cup.
The Spanish midfielder collected a loose ball inside the box and beat Dean Henderson from a narrow angle - just when it seemed the home side had forced extra-time.
David McGoldrick had equalised just moments before when we failed to deal with a long throw-in and Sead Kolasinac's attempted clearance hit Shkodran Mustafi.
Nicolas Pepe's penalty had given us a first-half lead after Alex Lacazette was clattered just inside the area as he controlled a pass from Kieran Tierney.
That opening goal came against the run of play after a difficult spell that saw Sheffield United get the ball into the net - only for John Lundstram's header to fall victim to VAR.
We grew into the game though, and Pepe forced Henderson into a tremendous one-handed save after good interplay with Lacazette.
The impressive Tierney set up our next chance with a perfect low cross that Pepe whipped just wide of the near post.
We finished the first half on the front foot, but the hosts piled on the pressure after the break.
Once again we were indebted to the offside flag - this time McGoldrick was penalised as John Egan converted from close range.
Chris Basham headed a great chance wide but we remained a threat too, with Tierney providing an outlet and ammunition from the left.
Mikel Arteta freshened us up with a string of substitutions but then McGoldrick pounced - only for Ceballos to have the final word.
HOW IT HAPPENED
FOUR THINGS WE NOTICED
WHAT IT MEANS
We go into the draw for the last four of the Emirates FA Cup. The semi-finals will be placed behind closed doors at Wembley over the weekend of July 18 and 19
Arteta made five changes to his starting line-up.
David Luiz was back in the side after his two-match suspension and Ainsley Maitland-Niles, Joe Willock, Kolasinac and Lacazette joined him.
Mesut Ozil was ruled out with a slight back injury.
We're back in Premier League action on Wednesday with our first home game since the restart - against Norwich City.
Copyright 2021 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source.