A combination of Jordan Archer's brilliance and 60 seconds of carelessness prevented Sheffield United from winning this absorbing match.
Chris Wilder's team appeared destined to claim all three points when Leon Clarke pounced during the closing stages but, as Bramall Lane erupted, Steve Morison kept his cool and levelled almost straight from the restart.
Wilder, who can have no complaints about his players' desire, will nevertheless be disappointed with the defending which allowed the Millwall centre-forward to pounce. Neil Harris' side showed why they are also challenging for promotion but, with Archer making numerous fine saves, spent long periods of the contest being pushed back.
United, with only three fixtures of the season remaining, still possess a more than mathematical chance of a top six finish. However, the reaction of the two squads at the final whistle confirmed which of them the result suited best.
When United returned to the dressing room for the interval, a pattern had already begun to emerge. The hosts, behind Harris' men in the table, were more intent on forcing the issue. Millwall could hardly be described as placid but, given the state of play in the Championship, it was clear a draw suited them more.
The introduction of Mark Duffy at the beginning of the second period brought a different dimension to United's work. Likewise when Billy Sharp replaced David Brooks just before the hour.
Wilder was clearly determined to try and force the issue but, as a consequence, his team's play became increasingly ragged. You could not argue with the tactics or, for that matter, be too critical of United's decision to rush and hurry. It was merely a reflection of the circumstances.
Finally, with a quarter-of-an-hour remaining, the contest which had been simmering just below the surface broke the waterline.
Clarke sent shockwaves through the stadium when, after tracking Jack O'Connell's header following Lee Evans' cross, his 18th goal of the season fired United in front. But, as United contemplated arguably their most significant victory of the campaign so far, Millwall took advantage of a lapse in concentration to equalise within 60 seconds. After finding himself in acres of space from a routine ball forward, Morison could scarcely believe his luck.
Big games demand big calls and Wilder made two before kick-off. Goalkeeper Jamal Blackman made an immediate return following suspension while Richard Stearman featured at centre-half after recovering from injury. Given the size of the prize potentially at stake, both sides could have been forgiven for attempting to ease themselves into the fixture. But, as Wilder had predicted beforehand, neither his team nor Millwall know the meaning of the phrase 'half measures.'
The first chance did not come until the 8th minute, when Evans saw a long-range effort fly inches wide, but there were plenty of good intentions from both during the seven which preceded it.
Having watched his fellow midfielder score twice against Middlesbrough earlier in the week, John Fleck also looked to test Archer in the 14th minute but a deflection took the sting out of his shot. With fast and direct counter-attacks a feature of Millwall's play, O'Connell was required to make a crucial tackle soon after. His challenge on Lee Gregory, a former United trainee, might not have been the hardest or most eye-catching of his career. But, with Jed Wallace in acres of the space inside the penalty box, there could have been serious repercussions if the ball had made its way across Blackman's area.
United's response came in the shape of impressive cameos from Leon Clarke, who did well to hold-off his marker, turn and flash a low drive across the box, and Fleck. The latter's driving run punched a hole through Millwall's defensive line but his shot again flew straight at Archer.
Five minutes after half-time, George Baldock was left ruing the Millwall goalkeeper's agility when he turned his attempt over from close-range following O'Connell's cross. Brooks also enjoyed a brief sight of goal but, struggling to adjust his feet inside a crowded area, was duly robbed of possession.
At the other end, in the 63rd minute, Blackman made a fine save to deny Jake Cooper following a Millwall corner before Archer breathed a sigh of relief when Clarke could not quite get a clean enough connection on a far post header. Duffy surged forward in the 70th minute but, with his options limited, dragged a low shot wide of the post.
Clarke, however, made no mistake five minutes later after Evans and O'Connell combined. But, less than 60 seconds later, Millwall levelled when Morison converted a simple chance.
Sheffield United: Blackman, O'Connell, Stearman (Lafferty 71), Basham, Stevens, Baldock, L Evans, Fleck, Lundstram (Duffy 46), Brooks (Sharp 58), Clarke. Not used: Moore, Donaldson, Wright, Leonard.
Millwall: Archer, Meredith, Hutchinson, Williams, Romeo, Wallace, Saville, Cooper, Marshall (Ontedinma 84), Gregory (Elliott 90), Morison. Not used: Cahill, Martin, Tunnicliffe, O'Brien, Shackell.