Gaetano Berardi was controversially sent off after just 14 minutes at The Den with referee James Linington awarding the hosts a penalty. Jed Wallace converted before Bradshaw doubled the lead on the stroke of half-time. Gjanni Alioski gave Leeds a lifeline after the break but Marcelo Bielsa's men left the capital pointless for a second straight week.
Millwall - same result, but a different feeling
Defeat at The Den is a familiar feeling for Leeds, but Saturday's loss had a sense of injustice for United fans.
Leeds last left Bermondsey with all three points in 2012, with a run of one point from six outings following that win over seven years ago.
Gaetano Berardi's early red card put paid to the Whites challenge of breaking their poor run against the Lions on home soil.
Gjanni Alioski briefly reignited belief with a goal just 15 seconds following the interval, but Bielsa's men failed to make their domination count in the second half with a man less.
James Linington's decision to hand Berardi his marching orders will be appealed by Leeds on Monday morning, and replays suggest that the Elland Road side have a strong case.
Leeds have wilted away at Millwall in the past, but this weekend's defeat was over before it even begun handing Leeds a similar result but not a familiar feeling as they headed back to West Yorkshire pointless.
Ben White oozes class
Whatever is thrown at Ben White the loanee seems to answer.
Another calm and assured display in the heart of defence for White in difficult circumstances as the Brighton loanee helped United assert control over Millwall, despite the Lions having a man advantage.
White has taken to the Championship like a duck to water, and seems to be going from strength to strength under Bielsa.
Leeds will need the 21-year-old to step up again as defensive injuries pile up with the Whites now also facing an anxious wait over Berardi's forthcoming appeal.
Bielsa post-match - reading between the lines
Marcelo Bielsa doesn't comment on match officials, a policy he has always maintained since his arrival in LS11.
Reading between the lines though, it's not hard to see how much he believed officiating had an impact on proceedings at The Den.
He said post-match: "There were three important situations in the match: the penalty, the red card and the next situation where [Jack] Harrison (went down in the box).
"Those three actions you can judge on the television. I prefer to analyse the game and not the referee."
Andrea Radrizzani sums up the feeling
United owner Andrea Radrizzani summed up the feeling in the Leeds camp afterwards.
The Whites were visibly down following the defeat post-match, and the chairman decided to send a message to the supporters on social media following the game.
"It's frustrating to see how many points we miss because of wrong decisions against us," Radrizanni tweeted.
"We will fight hard and come back stronger... we can’t just wait for VAR to reach our goal. #MOT"