The Blades have blown either hot or cold in an inconsistent season, with only two of their 28 league games prior to Saturday finishing level – and zero away.
But they were well worthy of their point and could have taken all three back up to Bramall Lane if not for O’Hare’s profligacy.
The visitors were, however, grateful to goalkeeper Michael Cooper for a fine one-on-one save from Macaulay Langstaff, sent racing clear by Ivanovic, to prevent Millwall taking an early lead.
The Blades capitalised on that let-off with an opener that owed much to Gus Hamer’s tenacity in winning possession – but there was still much for Brooks to do as he dropped a shoulder and steered home left-footed from the edge of the box.
Millwall, though, were quickly level as Ivanovic stole in to flick his seventh goal of the season past Cooper from six yards after Caleb Taylor headed Alfie Doughty’s deep free-kick goalwards.
Both teams lost players to heavy challenges either side of the interval, Blades defender Sam McCallum taken off on a stretcher before the break while Doughty later limped off for Millwall.
In between, O’Hare somehow headed wide with the goal gaping after Millwall keeper Max Crocombe saved well from Tom Cannon’s shot.
O’Hare again spurned arguably the best chance of the second half, failing to make a true connection from Femi Seriki’s inviting cross as Crocombe gathered gratefully.
Millwall introduced newest signing – and Sheffield Wednesday legend – Barry Bannan off the bench for his debut in search of a headline-grabbing winner and he did have a chance amid late Lions pressure but it was a routine save for Cooper.