Orla Murphy, 21, with an address at Ballinacarrig, Whitechurch, Co. Cork and 23-year-old Oxford University biology student Zachery Lumley, from South Lodge Ballinlough, Cork City, were each fined €2,000, and both must pay €2,000 in compensation to the State before December 1.
Gardai arrested them on the afternoon of March 19 last year.
They were charged with criminal damage at Simon Coveney’s department building, Iveagh House, St Stephen's Green, Dublin 2.
Lumley filmed as Murphy splattered and sprayed red and pink paint on the front of the building.
Posters were also stuck to the wall of the building, and the incident caused €4,300 worth of damage.
They pleaded not guilty at Dublin District Court and used a "lawful excuse" defence based on a sincerely-held beliefs their actions were necessary to protect lives at risk from the climate crisis.
However, on Tuesday, Judge John Hughes rejected their points and held it was "an audacious and shocking act which did cause damage to one of the finest buildings in the country".
He said they acted in a joint enterprise. Convicting them, he held they live-streamed the premeditated 10-minute incident "to get notoriety and publicity". He noted that public members were shocked by what they saw and attempted to intervene to no avail.
Arresting gardai Philip Farrissey and Paul Cummins told the court they received reports of the incident and arrested the pair at the scene. Statements were taken from shocked eyewitnesses. Murphy told one of them that spray painting was the only way "to get the message out" about the planet's future.
Gardai obtained CCTV evidence from the building and seized Murphy's paint-stained clothing, and Lumley's shoes also had matching paint underneath.
Garda Farrissey said Lumley filmed and "egged on" Murphy, who also had paint tins in her backpack.
He asked them why and was told it was about climate change. There had been a letter-writing petition to the Department of Foreign Affairs, "but nothing came of that".
Zachery Lumley told the court he had been terrified of the climate crisis since he was 10 when he obsessively began switching off taps and lights. He said he had become a member of Extinction Rebellion and other environmental groups.
He explained that they chose Simon Coveney's department because Ireland was on the UN security council, which has a role in preventing loss of life. But he maintained that "climate change is the greatest risk to human life".
Murphy, who has completed two years in a media course, told the court she learned about protesting and civil resistance first in school and later from books. She believed throwing paint was a proportionate form of "direct action" due to the number of people dying due to the climate crisis.
Cross-examined, they disagreed with the prosecution that their actions would not have protected anyone.
The State also submitted that the defence argument was a “vandal’s charter”.
They had no prior convictions.
Pleading for leniency, defence counsel Katie Glennon said the defendants had suffered from depression but had bright futures and caused no permanent damage.
Lumley, who works part-time in a restaurant, offered to pay the cost of repairs and to stay away from "more radical elements".