Cairney's first-half goal was decisive as Fulham, owned by U.S. billionaire Shahid Khan, held on to their narrow lead despite having defender Denis Odoi sent off after 70 minutes as tempers began to fray on a sultry afternoon.
The win secures the west London club a windfall of at least 160 million pounds ($212.91 million) as they look forward to joining Championship title winners Wolverhampton Wanderers and second-placed Cardiff City in the top flight next season.
Fulham, who failed to claim automatic promotion when losing to Birmingham City on the final day of the regular season as they finished third in the table, celebrated with their joyous fans as they sealed a lucrative place among the elite.
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"After we missed out on promotion (in the playoffs) last season, a lot of people wrote us off. We got a lot of stick. But football won today. Football was the winner," Cairney said.
With the stakes so high it was no surprise that the match was a frenetic affair in the opening stages.
Fulham, whose style of play under Serbian manager Slavisa Jokanovic earned plaudits this season, were the first to settle and scored from the game's first piece of quality football.
Teenager Ryan Sessegnon received the ball midway inside Villa's half, evaded a tackle, and turned to play a through ball that Cairney calmly slotted past keeper Sam Johnstone.
VILLA RESPOND
Villa, led by former England and Chelsea defender John Terry, were dreadful in the first half but they revived after the break.
Jack Grealish suddenly got involved in the game and he forced a save from goalkeeper Marcus Bettinelli after a superb slaloming dribble through the Fulham defence.
Villa also had a penalty appeal turned down but Grealish was lucky to escape a red card with a reckless tackle on Cairney.
Odoi's clumsy attempt to win the ball off Grealish earned him a second yellow card and left Fulham to survive the last 20 minutes and five minutes of stoppage time with 10 men.
Villa threw everything forward in the nail-biting closing stages but Fulham held on without too many alarms.
Defeat ended Villa manager Steve Bruce's hopes of a record fifth promotion to England's top flight.
According to the Deloitte Sports Business Group, the playoff winners are guaranteed 160 million pounds, potentially rising to 280 million if they avoid relegation next season.
Fulham will earn 95 million pounds next term, as part of the Premier League's huge broadcasting rights deal, and up to 75 million pounds in parachute payments in 2019-20 and 2020-21 should they fail to stay up.
(Reporting by Martyn Herman; editing by Ken Ferris)
