With the toothless home side having barely fashioned a chance, Scottish international Andy Robertson sealed the visitors' triumph deep into stoppage time with a fine shot after a swift counter-attack.
The surprisingly comfortable win leaves Hull in the driving seat with the second leg at their KCOM Stadium on Tuesday.
No team have overturned a two-goal first-leg deficit in a Championship playoff so, with Sheffield Wednesday beating Brighton & Hove Albion 2-0 in the opening leg of the other semi on Friday, an all-Yorkshire final at Wembley looms on May 28.
Hull finished fourth in the regular season, five points and one place ahead of Derby, and Steve Bruce's side quickly demonstrated their superiority after a bright start from the hosts when Hernandez fired a low shot past Scott Carson.
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The former England goalkeeper looked slow to get down to the strike but there was nothing he could do about the second goal when he was left helplessly stranded as Moses Odubajo's shot was redirected by two deflections, the last off Shackell.
Robertson added Hull's third goal eight minutes into added time leaving shell-shocked Derby, the only team to win a league game at Hull in the regular season, with a mountain to climb.
(Reporting by Ian Chadband; editing by Ken Ferris)
