Leeds has a one-point advantage at the top of the table, with Brentford and Bristol City capitalising on a slip-up from Middlesbrough, which lost at Norwich City, to move above Tony Pulis' side into second and third place respectively.
Meanwhile, Derby County's winning streak was halted by Rotherham United, with Tom Lawrence seeing red before manager Frank Lampard was sent to the stands.
Elsewhere, Stoke City's dismal run continued — it remains just a point above the relegation places after squandering a two-goal lead against Sheffield Wednesday — while Reading enjoyed its first win of the season at Preston North End.
Bielsa-ball looked to have met its match when the Whites' arch-rival Millwall took the lead at The Den, Jed Wallace heading the hosts in front in the 55th minute.
Leeds refused to give in, though, and it was on-loan Manchester City youngster Harrison who snatched the equaliser in the final minute of normal time with his first goal for the club.
There would be more drama in stoppage-time when Millwall's Tom Elliott hit the post before seeing an appeal for a penalty dismissed, but Leeds held firm to hang on to top spot and keep its unbeaten record under Bielsa intact.
BRENTFORD, BRISTOL CITY MAKE THE MOST OF BORO'S SLIP-UP
While Leeds managed to maintain its unbeaten record, Middlesbrough was not so lucky, as Teemu Pukki's effort claimed the points for Norwich City at Carrow Road.
Pulis' side is now one of three sides on 14 points, with Brentford having taken its place in second after a 2-0 home victory over Wigan Athletic, Neal Maupay at the double.
Substitute Marley Watkins proved the hero at Ashton Gate, however, as his 81st-minute header brought Sheffield United's four-game winning streak to an end, lifting Bristol City into the top three in the process.
Derby County was on a roll heading into its clash with Rotherham United at New York Stadium, with three successive wins taking Lampard's side into the top six.
But it proved a frustrating trip to South Yorkshire for the Rams, and a difficult game was made harder when playmaker Lawrence was shown a straight red card for fighting midway through the second half.
Matters were made worse five minutes later when Ryan Manning converted from the spot after Craig Forsyth's foul on Richard Wood and, to cap it all off, Lampard received his marching orders late on.
OWLS FIGHT BACK, READING GET OFF THE MARK
Stoke City is not adjusting well to life in the second tier, but Benik Afobe's double put the Potters in cruise control by the 22nd minute at Hillsborough.
Sheffield Wednesday swiftly pulled one back through Marco Matias, and the pressure finally told on the Potters with eight minutes remaining when Barry Bannan curled in a free-kick.
Meanwhile, Reading finally tasted victory in dramatic style, as Leandro Bacuna's late strike secured a 3-2 victory against Preston North End to lift Paul Clement's side off the foot of the table.