Three protesters sped onto the ground five minutes after the start of play at the home of cricket on Wednesday, forcing players to stop them from throwing orange powder on the pitch.
One was apprehended by Bairstow, a keen rugby league player in his youth who frogmarched the protester 50 metres to the boundary.
Another had to be wrestled to the ground close to the wicket as Ben Stokes and David Warner, who had his bat in hand, attempted to tackle him. A third protester was apprehended in the stands, as all three were arrested.
The incident prompted a delay of five minutes as the ground staff cleared some of the powder from the outfield, after England had won the toss and sent Australia in to bat.
Officials have been concerned about the threat of protesters disrupting Test matches this summer and the potential of matches being abandoned if pitches are destroyed.
Several major sporting events, including premier league matches, the premiership rugby final at Twickenham and World Snooker Championships in April have been targeted by activists.
England's team bus was also held up by the protesters during the Lord's Test against Ireland earlier this month.
Australia captain Pat Cummins, who has been vocal in his push for action against climate change, pleaded with protesters not to target pitches at the start of the tour.
"My view is always just there's right ways to go about things and potentially not the right way to go about things," Cummins said.
"Whenever anyone's got any beliefs, you just hope you take the right option."
Curators have prepared a back-up pitch in recent Tests in England in case the main one is damaged, however that would significantly change match conditions.
But even though there was a strong likelihood of play being interrupted by a protest, what was most remarkable was that it ended up being largely down to the players' own initiative to prevent the demonstrators from spilling powder onto the pitch as security appeared slow to react.
Bairstow handed his protester over to the stewards, before heading to the pavilion to change his whites, but his actions surely stopped a lengthier stoppage.
The other protester, who attracted the attention of England captain Stokes, was intercepted by security staff, while another was apprehended in the stands.
Broadcasters largely chose not to highlight the incident, but Ricky Ponting couldn't resist a jokey reference to Bairstow's first-Test wicketkeeping woes.
"I didn't want to say anything, but the one chance that's come Jonny's way, he's held on to so far," the former Australian captain said on Sky Sports.
A spokesperson for the Metropolitan Police reported: "Police have arrested three people and taken them into custody."
Guy Lavender, chief executive of the Marylebone Cricket Club, which owns Lord's, said: "MCC condemn in the strongest possible terms today's pitch incursion and with the behaviour of the protesters involved.
"Their actions not only endanger themselves and those who work at the ground, but they have consistently shown complete disregard for the people who pay to attend events, not just here at Lord's but around the country at other sporting venues."
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