Having only ever reached the competition's final four once in their history, Hull dominated much of the game and ultimately deserved their comfortable triumph.
Nerves at the KC Stadium will have been jangling at half-time after Oscar Ustari's save from a poor first-half Sone Aluko penalty.
However, the hosts kept the pressure on after the interval and booked just a second trip to Wembley in their history, after their Championship play-off final win in 2008, through Curtis Davies' towering header and David Meyler's counter-attack effort.
Lee Cattermole then gifted Matt Fryatt a late third with a terrible backpass - the striker netting his third cup goal of the campaign.
Sunderland were looking to visit the national stadium for a second time this season, after last week's League Cup final defeat to Manchester City, but toothlessness in attack cost them dearly.
Ustari was almost caught out early on as a mis-hit Maynor Figueroa cross drifted over his head and clipped the crossbar, while Fryatt - leading the line in the absence of cup-tied duo Shane Long and Nikica Jelavic - saw a stooping header drift narrowly wide.
The hosts had largely dominated the opening half-hour and were presented with the chance to go ahead on 34 minutes when Sebastian Larsson tripped Aluko in the penalty area, but the Nigerian's weak attempt was well-saved by Ustari to his right.
Emanuele Giaccherini almost made the hosts pay immediately afterwards, curling an effort wide, and Ustari further proved his worth by tipping away Liam Rosenior's 30-yard drive before the break.
The second period continued in the same vein with Sunderland looking to soak up waves of Hull pressure, but they were finally broken down with 69 minutes on the clock as Davies rose highest and thudded home a Tom Huddlestone free-kick.
Just three minutes later, Steve Bruce's first cup semi-final as a manager edged closer as Meyler latched onto substitute George Boyd's clever flick and kept his composure having ran through the Sunderland half unopposed to slot past Ustari.
The Ireland midfielder capped the goal by nudging the corner flag with his head in celebration - apparently making light of Newcastle United boss Alan Pardew's headbutt on him a week previously.
Fryatt added the gloss after being played in by Cattermole's catastrophic backpass, and Hull will hope their impressive season back in the Premier League will be lit up by Wembley success next month.
