The hosts dominated the first half and went in with a deserved 2-0 lead courtesy of Aaron Mclean's opener and Cairney's memorable strike from 25 yards.
Ipswich substitute Jason Scotland took advantage of Vito Mannone's error to pull one back for Town but Cameron Stewart sealed the win in injury-time with a clinical finish.
Both sides made changes for the match, with seven alterations to the Hull side that lost to Derby, while Ipswich boss Paul Jewell brought in four new faces from the defeat to Nottingham Forest.
Mannone was in the Hull goal, starting his second spell at the club on loan from Arsenal, but there was no return to the KC Stadium for Town midfielder Jimmy Bullard, missing with illness.
Hull were first to settle in the match, Robbie Brady and Stewart linking well before one over-hit pass released the danger.
Ipswich hit back and almost took the lead in the fifth minute when Daryl Murphy just failed to get on the end of Arron Cresswell's cross.
The Tigers raised the pressure soon after, Brady with a dangerous free-kick and Stewart going close -with a drilled near-post effort.
Mclean was next to cause some alarm for Ipswich after 15 minutes when his deep cross drifted goalwards and needed to be tipped over by Arran Lee-Barrett.
Richard Garcia went close to breaking the deadlock after 25 minutes, Stewart cutting into the box from the left before sending a low cross along the six-yard line.
With his back to goal Garcia cleverly flicked the ball towards the back post with his instep only to see it squirm wide.
Moments later Hull had the lead, Brady surging into the final third before laying the ball off for McLean, who outmuscled Ibrahima Sonko and poked his shot past Lee-Barrett.
Cairney added a superb second after 32 minutes, collecting Stewart's pass, shifting the ball to his left foot and expertly catching the goalkeeper off his line from 25 yards.
Most of Jewell's starting XI had forgettable first halves but it was striker Nathan Ellington who paid the price at half-time, with Scotland coming off the bench.
The Trinidad and Tobago international took 12 minutes to get his side back into the game with a simple finish. Jay Emmanuel-Thomas tried his luck with a hopeful long-range effort which Mannone dealt with poorly, pushing tamely to Scotland who tucked away first time.
Hull had been coasting after the restart but were now forced to up the tempo.
Ipswich were also looking a little brighter and would have been level after 68 minutes had Emmanuel-Thomas produced a better finish when the nervy Mannone failed to come for a ball over the top.
Seyi Olofinjana came on to hold the Hull midfield for the last 20 minutes, while the visitors summoned Michael Chopra from the bench.
He had an early chance to strike at goal but blazed high and wide from 12 yards.
The Tigers were hanging on by now and Josh Carson drew a diving save from Mannone with a well-struck effort from 25 yards.
Grant Leadbitter almost grabbed the equaliser in added time but instead Mannone clung on and Hull rubbed it in with a breakaway third, well finished by the impressive Stewart.