Roger Hallam and other protesters wanted to shut down the busy aviation hub to publicise their opposition to the construction of a third runway, their trial at a court in west London was told.
But police swooped to thwart the climate activists' plans, throwing up a sweeping security cordon and making several arrests.
Hallam, 57, was found guilty by a jury at Isleworth Crown Court of conspiracy to cause a public nuisance after a four-week trial that ended in December.
Co-defendant Larch Maxey, 51, was convicted of the same charge, while a third protester, Michael Lynch-White, 33, pleaded guilty. A fourth protester was cleared.
Prosecutors said the trio did not want to cause a crash, harm or endanger the public but instead cause "chaos", with the aim of shutting Heathrow until the government reversed its backing for a third runway.
The defendants said they only wanted to attract publicity for their protest, which was motivated by concern about climate change and called Heathrow Pause.
Judge Martin Edwards said a small number of drones flown during the protest in September 2019 did not disrupt flights.
He sentenced Hallam and Maxey to two years in prison, suspended for 18 months. Lynch-White was given a 17-month jail term, suspended for 18 months.
All three were also ordered to carry out unpaid community work.
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