Top marksman Aleksandar Mitrovic stretched the Fulham advantage to 3-0 before the half-hour mark.
He pounced twice from close range to take his tally for the season to seven.
Cairney added his second goal, his fifth of the term, in the 67th minute after an error by home goalkeeper Rafael.
Yakou Meite thumped home a 20-yard shot for Reading one minute from time but Fulham won at a canter.
After three successive 1-1 draws, Fulham had defeated Wigan 2-0 at Craven Cottage last Friday and Reading were winless in five outings in all competitions.
The contest got off to a frantic start, with Bobby Reid shooting over for Fulham from 20 yards.
Reading replied quickly, with visiting goalkeeper Marcus Bettinelli having to save smartly from Meite's angled effort.
Swift then made a rash challenge on Reid, which sparked a melee involving most of the players.
Referee Andy Woolmer calmed the situation and issued Swift with only a yellow card.
Fulham's growing authority was rewarded in the 13th minute when they went ahead through Cairney.
Stefan Johansen's pass created the space on the edge of the home area and Cairney curled home his third goal in successive matches past Rafael.
Seven minutes later, it got worse for Reading. Swift arrived late on Fulham right-back Denis Odoi and was shown a second yellow card, then red, by Woolmer.
Fulham responded to their numerical advantage by scoring twice through Mitrovic.
The Serbia striker first turned in a low cross from the right from Anthony Knockaert in the 26th minute.
Three minutes later, he guided home past Rafael with ease from a Joe Bryan centre from the left.
Fulham eased off approaching half time but should have made it 4-0 in the opening stages of the second period.
Knockaert was left free in the home area but his dinked effort was beaten away by Rafael.
Reading made a rare excursion forward, with George Puscas going on a mazy run before driving wildly over.
Fulham retaliated with a fierce drive from centre back Alfie Mawson that Rafael saved superbly low down.
Mitrovic could have completed his hat trick but headed wide when unmarked from a Johansen cross.
But Fulham made it 4-0 in the 67th minute when Rafael's attempted clearance was blocked and Cairney cleverly lobbed the ball over him into the empty net.
Meite's powerful left-footed drive in the 89th minute was no more than a minor consolation for Reading.