Fulham return to the top flight of English football after a four-year absence, but Villa will spend a third campaign in the second tier after failing to find an equaliser in the second half.
As expected, it was Fulham who set about retaining possession - which Villa were happy to give their opponents - but the Cottagers initially struggled to create chances in the final third.
The first opportunity did not arrive until the 21st minute when Aboubakar Kamara turned off John Terry before attempting a volley on the edge of the area, but the winger's weak effort was helped over the crossbar by Sam Johnstone.
However, two minutes later, Fulham were ahead. Ryan Sessegnon retrieved the ball before playing a perfectly-weighted pass through to Cairney, whose calm finish from 10 yards went past Johnstone and into the bottom corner.
Fulham quickly pushed for a second but on the half-hour mark, defender Ryan Fredericks may have been sent off for standing on the knee of Jack Grealish after a challenge on the touchline, only for the referee and fourth official to miss the infringement.
The West Londoners could have added a second through Sessegnon - who headed straight at Johnstone from eight yards out - but Villa should have been level with five minutes of the first half remaining when Grealish volleyed over from 10 yards after a clever free kick from Robert Snodgrass.
After the break, Villa immediately showed an improvement but again, Grealish wasted a chance to bring his side level when heading over from just eight yards after meeting a cross from Albert Adomah.
Back up the other end, Aleksandar Mitrovic glanced a header wide of the far post but Villa were quickly back onto the offensive and Grealish came agonisingly close to scoring one of Wembley's great goals.
The academy graduate picked up the ball around 35 yards out before gliding past four Fulham players who came his way but, after getting to within 10 yards of goal, the winger's resulting shot took a slight deflection and was superbly blocked by Marcus Bettinelli.
Villa soon began to tire and both Kevin McDonald and Stefan Johansen wasted chances inside of the penalty area, but just as it appeared that Villa were there for the taking, Fulham were reduced to 10 men after Odoi picked up a second yellow for a foul on Grealish, just minutes after the attacker should have been sent off for a crude tackle on Cairney.
The dismissal resulted in tactical changes from both Steve Bruce and Slavisa Jokanovic but despite being down to 10 men, Fulham continued to show ambition going forward with Mitrovic seeing a volley from close range deflected over the bar.
Villa were in the ascendancy for the closing 15 minutes but their sole chance before five minutes of added-on time came through Snodgrass, who curled a free kick just wide of the post.
Scott Hogan also glanced a header wide of the far post and it proved to be Villa's last effort as Fulham secured a deserved return to the top flight after relegation to the Championship in 2014.
ASTON VILLA (4-5-1): Johnstone; Elmohamady (Kodjia 77'), Chester, Terry, Hutton; Jedinak (Onomah 77'), Hourihane (Hogan 82'); Snodgrass, Adomah, Grealish; Grabban
FULHAM (4-3-3): Bettinelli; Fredericks (Christie 83'), Odoi, Ream, Targett; McDonald, Cairney, Johansen (Norwood 72'); Kamara (Kalas 77'), Sessegnon, Mitrovic