The Prime Minister hailed the England wicketkeeper’s “swift hands” and the actions of Ben Stokes’ team in preventing a prolonged stoppage in the game.
Three people were arrested and taken into custody after Wednesday’s pitch invasion, the Metropolitan Police said.
The climate change group has been staging daily protests since April 24, disrupting high-profile events like the Chelsea Flower Show, the Gallagher Premiership rugby final at Twickenham and the World Snooker Championship, as well as holding daily slow marches on major London roads.
Mr Sunak’s official spokesman said: “These sorts of selfish, guerrilla tactics that target events bringing joy to millions are exactly why the Government brought in new powers so the police can take swift action.
“The Prime Minister is pleased play was able to resume quickly and thanks security staff, the swift hands of Jonny Bairstow and other England players who stepped in.”
Just Stop Oil’s actions have led some frustrated motorists to take matters into their own hands in the same way as Bairstow, but Downing Street said the situation at Lord’s was an unusual one and dealing with protests should usually be left to the police.
“There is a reason we empowered the police to take action and that’s what we see day-to-day,” Mr Sunak’s spokesman said.
“Obviously these were unusual circumstances.”
Two people were seen being put into the back of a police van outside the London ground after the on-pitch drama.
Just Stop Oil is calling for an end to all new coal, oil and gas projects in the UK.
A spokesperson said: “Cricket is an important part of our national heritage, but how can we enjoy England vs Australia when much of the cricketing world is becoming unfit for humans to live in?
“We can no longer afford to distract ourselves when the sports we play, the food we eat and the culture we cherish is at risk.
“It’s time for cricket lovers and all those who understand the severity of this situation to get on to the streets and demand action from this illegitimate, criminal Government.
“When our children ask us, ‘What did we do?’ to avert this crisis, we better have a good answer.”
The group said a 69-year-old grandmother called Judit was one of those arrested.
On Monday, Metropolitan Police Assistant Commissioner Matt Twist told LBC that policing the action has cost £5.5 million since April, on top of the £7.5 million spent policing the series of protests Just Stop Oil staged between last October and December.
Earlier this month, protest laws were tightened up to allow officers to intervene earlier when protesters are marching in the road, forcing them on to the pavement where disruption is felt to be more than minor.
The Ashes pitch invasion is not the first time Bairstow has had to deal with disruption to play.
In 2021, during the fourth test against India at the Oval, YouTube prankster Jarvo ran on to the pitch and collided with an unsuspecting Bairstow.
Jarvo, whose real name is Daniel Jarvis, was found guilty of aggravated trespass and given a suspended prison sentence.