Bairstow was given out when Australia wicketkeeper Alex Carey threw the ball at the stumps after the England batsman walked out of his crease after ducking under a Cameron Green bouncer.
There was confusion in the middle, Bairstow seemingly believing the ball was dead at the end of the over but Australia were happy to proceed with a deeply divisive appeal.
The umpires sent the decision upstairs for review by TV umpire Marais Erasmus, who had no option but to confirm Bairstow's stumping dismissal.
Bairstow was livid and the usually sedate Lord's crowd responded by chanting "Same old Aussies always cheating" while booing rang around the famous old arena for several minutes.
England's Stuart Broad, the batsman who came in after Bairstow's exit, immediately let his frustrations show as the stump microphone caught him telling Carey: "That's all you'll ever be remembered for that."
Broad also shouted at Australia captain Pat Cummins, ranting "That's the worst thing I've ever seen in cricket".
The England pace bowler kept up his barrage as he exchanged angry words with Australian fielders and mockingly tapped his bat in his crease after each delivery to ensure he didn't depart the same way as Bairstow.
A bitter row about the 'spirit of cricket' was underway, with furious fans chanting "cheats" and England's players clearly angry Australia did not withdraw their appeal on grounds of fair play.
Members in the Lord's Pavilion, the most prestigious stand in the stadium, confronted the Australia team as they walked through the historic Long Room to get to their dressing room at lunch.
Australia batsmen David Warner and Usman Khawaja were seen stopping to speak to members who were booing before stewards stepped in to usher the players away.
The controversy came amid England's bid for a Lord's record run chase of 371 to win the second Test.
England captain Ben Stokes was unbeaten on 108 and Broad was one not out as the hosts reached 243-6.
