The district judge also banned the trio -- two men in their twenties and a 69-year-old woman -- from going near the famous London ground for a year, as part of 12-month community service orders.
The Just Stop Oil protesters must each complete 60 hours of unpaid work, and each pay 330 pounds ($400) in punitive costs.
They were found guilty last month of "aggravated trespass" following their stunt, which briefly interrupted play on the first day of the second Ashes Test between England and Australia.
Two of the demonstrators sprinkled orange powder on the square but not the pitch at the hallowed home of English cricket. Wicketkeeper Jonny Bairstow wrestled one of them to the ground.
A third demonstrator was tackled before making it onto the outfield.
It was the latest UK sports event to be disrupted by the so-called direct action environmental pressure group, following similar protests at spectacles including golf's British Open and the Wimbledon tennis championships.
Sentencing the trio, district judge Neeta Minhas accepted no damage had been caused to the pitch but noted there were serious implications from their actions.
"It also causes difficulty for security at that venue who have to control the crowd," she said.
"It also takes security away from doing the job that they're supposed to be doing, while they are detaining you and ensuring your safety from the crowd."
Just Stop Oil wants an end to new oil and gas exploration in the North Sea.
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