Meyler headbutted the corner flag in celebration after sweeping home the second of his side's three strikes which turned a largely dismal FA Cup last-eight tie into one of celebration for the home side, who cantered to a 3-0 win and the chance to face Sheffield United in the last four.
The hosts' captain Curtis Davies headed his side into a 68th-minute lead after rising highest to meet a Tom Huddlestone free kick, before Meyler supplied a cool finish four minutes later after chasing down a punt upfield from George Boyd.
And Sunderland's agony was complete in the 75th minute when Lee Cattermole, experiencing an afternoon to forget, played a shocking back-pass which left the lurking Matty Fryatt with the simplest of chances to score.
It could have been even worse for the visitors, who had to rely on goalkeeper Oscar Ustari saving Sone Aluko's 33rd-minute penalty in order to keep them level at the end of a largely forgettable first period.
Gus Poyet, the visitors' manager, will at least now be able to focus on his side's battle to stay in the top flight after the distraction of their knockout heroics, which also saw them lose 3-1 to Manchester City in the Capital One Cup final at Wembley last week. "We didn't create enough but I'm not going to try to find any excuses," he said. "The players who played today were not good enough and that is simple - in the 50-50s, in the diving, in dealing with the referee when he panicked for 10 minutes - in not recovering well and not creating one chance."
Steve Bruce, the Hull manager, was understandably pleased. "Managers, coaches and players come and go but the people you have got to be happy for is the supporters," he said. "It is quite remarkable that 1930 is the last time we were in a semi-final. I've said all along that it's sad that the FA Cup has lost a bit of the magic for whatever reason, but when you reach this stage it becomes exciting.
"I'm delighted for everyone. I've seen the scenes at Bramall Lane today and now we've got a big Yorkshire derby to look forward to."