One year on from a first league defeat of the season at Millwall under Thomas Christiansen, Millwall were a constant threat from set pieces and Leeds were undone in the 55th minute when a long throw led to Jed Wallace arriving in the area unmarked to provide a low finish in off the post.
Leeds looked to be heading for yet another defeat at The Den but Harrison produced a clinical low finish with just one minute left to keep United top with Middlesbrough losing 1-0 at Norwich City.
Leeds made a confident start and after Samu Saiz had skipped challenges from Wallace and Shaun Williams, Jack Harrison's cross flew narrowly infront of Gjanni Alioski at close range.
After Luke Ayling won a Whites free-kick some 25 yards out, Barry Douglas then curled an effort well wide of the left post before a raking cross from Harrison narrowly failed to pick out Tyler Roberts and Alioski.
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But Millwall then began to offer a real threat at set pieces with Ryan Leonard's header bouncing off Steve Morison into Bailey Peacock-Farrell's arms from a corner before Morison himself headed wide from another corner shortly after.
The returning Pontus Jansson was then let off the hook after giving the ball away with a loose pass in the centre circle as Millwall wasted the counter attack.
Leeds were under the pump though a fine pass from Mateusz Klich out wide to Barry Douglas led to a chance for Roberts whose shot from inside the area was blocked by Murray Wallace.
Millwall hit back - again through their aerial threat - with Morison's looping header just caught by Peacock-Farrell as the 'keeper scrambled back towards his own line.
But Leeds then squandered their best chance yet in the sole minute of first half-injury time when Roberts latched on to a long ball and outfoxed the backtracking Wallace only to see his shot hit 'keeper Ben Amos and trickle across the area to be cleared.
Leeds created the first opening of the second half but Saiz blazed over from the edge of the box.
Another golden opening then fell for Roberts who was played in at a tight angle by Alioski only to scuff his shot across the area.
From a well worked Leeds free-kick, Douglas then hammered a powerful volley from range straight at Amos.
But Millwall remained a constant threat from set pieces and in the air and the Lions made the breakthrough in the 55th minute when a long throw from Leonard was flicked on by Jake Cooper to Wallace who arrived completely unmarked to produce a low finish in off the post.
Leeds attempted to hit straight back and Amos produced a brilliant save to deny Ayling at a tight angle following a Douglas cross.
Saiz then teed up substitute Lewis Baker - on for Klich - who smashed an effort over the bar before another fine cross from Saiz picked out Roberts whose weak flicked header was easily saved.
Roberts was then taken off for Stuart Dallas who cut inside from the right and fired over before Bielsa made his final change in taking off Kalvin Phillips for Adam Forshaw, leaving teen forwards Jack Clarke and Ryan Edmondson on the bench with Harrison now playing upfront.
After Liam Cooper sliced a chance wide from a Douglas free-kick, United looked to be running out of time until a moment of magic from Harrison levelled matters in the 89th minute.
A long ball forward was headed clear by Jake Cooper but only into the path of Harrison who lashed home a fine low finish inside Amos' left hand post.
But even then the drama was not over with Millwall hitting the post in the second minute of injury time when a left hand cross found substitute Tom Elliott whose header bounced back off the woodwork.
Leeds then had to survive an almighty goalmouth scramble from a corner before the game ended with Conor McLaughlin rattling a fierce shot just wide.
Leeds United: Peacock-Farrell, Ayling, Douglas, Cooper, Jansson, Phillips (Forshaw 74), Klich (Baker 61), Alioski, Harrison, Saiz, Roberts (Dallas 68). Subs not used: Blackman, Pearce, Dallas, Edmondson, Clarke.
Millwall: Amos, McLaughlin, M Wallace, Cooper, Meredith; J Wallace, Williams, Leonard, O’Brien; Morison (Bradshaw 70), Gregory (Elliott 86). Subs not used: Martin, Romeo, Webster, Tunnicliffe, kalak.
Referee: Chris Kavanagh.