Just Stop Oil climate activists Anna Holland and Phoebe Plummer, both 22, were convicted of criminal damage at Southwark Crown Court in the British capital.
The pair had pleaded not guilty over the incident in October 2022.
The protest group, which wants an end to oil and gas extraction and use, has staged a number of high-profile stunts in recent years.
It has targeted the Wimbledon tennis tournament and British Open golf tournament, as well as art galleries and museums and a performance of "Les Miserables".
Several of its protesters were arrested at London's Heathrow Airport on Wednesday as activists staged co-ordinated action at airports across Europe.
Last week, five Just Stop Oil activists, including the climate group's founder, were given between four and five years in jail in the UK for conspiring to plan protests that blocked a motorway.
Just Stop Oil argues that climate change poses an existential crisis for humanity and that its direct tactics are justified.
The "Sunflowers" painting itself was protected by a screen but damage was caused to the frame, said the gallery, which is located in Trafalgar Square.
Holland and Plummer also glued themselves to the gallery wall during their protest.
"What is worth more -- art or life?" Plummer had shouted.
Earlier, in July 2022, Just Stop Oil protesters glued themselves to John Constable's pastoral masterpiece "The Hay Wain" in the National Gallery.
Holland and Plummer have been released on bail and will be sentenced in September.
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