Since going behind with half-time imminent, the Blades' attacking threat had been somewhat subdued, so Chris Wilder decided to pile substitutes on from the bench to do something about it.
Centre-forwards Billy Sharp and Callum Robinson were thrown into the fray, along with midfielder Mo Besic as Wilder went from his usual 3-5-2 formation to a midfield diamond.
And when Besic played Robinson in down the right, Sharp pressured Ainsley Maitland-Niles into a header that did neither one thing nor the other. John Fleck volleyed the equaliser in off the turf.
It was the Gunners who were relieved to hear the full-time whistle.
In truth, the equaliser had not been coming, but importantly the Blades held firm when they went 1-0 down. Their defensive resilience is one of many qualities that has put this side above Arsenal in the table.
The Blades missed two good headers early on. With David McGoldrick out with a foot injury, Lys Mousset was back in the side, but they could have done with the chances falling to his strike partner, Oli McBurnie.
Sheffield United were dangerous down their left in the early stages, and when Ainsley Maitland-Niles gave the ball away in the eighth minute, his cross picked out Mousset, who headed over.
He did the same two minutes later when Jack O'Connell headed John Fleck's corner to the striker. The flag was raised for offside, but television replays suggested video assistant referee Lee Mason might have had something to say about that had the ball found the net.
Arsenal steadied themselves and carved out a couple of good chances for Gabrieln Martinelli, but Pierre Emerick-Aubameyang's stand-in was wasteful too in the early stages.
Alexandre Lacazette was regularly dropping off the front, and in the 14th minute he played an excellent ball to Nicolas Pepe, the Gunners' chief first-half threat. His cross picked out Martinelli, who shot was horribly wide.
When Pepe found him again in the 21st minute, he pulled his shot wide.
Oliver Norwood volleyed miles over and Lucas Torreira produced a bouncing shot Dean Henderson got behind comfortably, but for the last 15 minutes, the half went a bit flat until Martinelli got third time lucky.
With half-time approaching, Arsenal produced an excellent move down their left, and when Bukayo Saka crossed, Martinelli drifted into space to gobble up a tap-in.
Sheffield United were sent out very early for the second half and although Enda Stevens put in a good low cross his team-mates could not quite stretch to, there was no barrage after the break. Granit Xhaka did have to clear O'Connell's header off the line from a 56th-minute Norwood corner, though.
Arsenal looked the more likely to score the second, Lacazette blazing a free-kick over before being replaced by Eddie Nketiah, recalled from a loan at Leeds United, who himself missed the target from a tight angle.
With 82 min utes gone, McBurnie's header at Bernd Leno from another corner reminded everyone the Blades were still in the contest, and a minute later they were on level terms.
McBurnie and Fleck had shots blocked in the 90th minute, while Besic forced a good save in stoppage time but the Blades can be pleased with their point.
Arsenal: Leno; Maitland-Niles, Mustafi, David Luiz, Saka; Xhaka, Torreira; Pepe, Ozil, Martinelli; Lacazette (Nketiah 74).
Unused substitutes: Bellerin, Ceballos, Holding, Martinez, Willock, Guendouzi.
Sheffiel United: Henderson; Basham (Besic 76), Egan, O'Connell; Baldock, Lundstram (Robinson 67), Norwood,
Booked at 4mins
Fleck, Stevens; Mousset (Sharp 56), McBurnie.
Unused substitutes: Jagielka, K Freeman, Verrips, Osborn.
Referee: M Dean (Wirral)