Millwall will have home advantage for the second leg at The Den as they aim to reach the top tier for the first time since 1990.
Alex Neil’s men finished 10 points ahead of The Tigers and will be frustrated at not taking a first leg lead after Ryan Leonard’s late goal was controversially disallowed.
Hull squeezed out Wrexham to make the top six on the final day of the regular league season last weekend.
The home side nearly had a dream start when Mohamed Belloumi hit the post after a brilliant individual run inside two minutes.
That was as close as Hull came as Millwall posed the greater threat of a tight encounter.
Camiel Neghli struck the woodwork and Femi Azeez was denied by a fine save from Ivor Pandur.
The biggest talking point came five minutes from time when Leonard prodded home, but the referee blew up for a perceived foul by Tristan Crama in the build-up.
Southampton travel to Middlesbrough in the other semi-final first leg on Saturday.
The winners of the two ties will face off at Wembley for a place in the Premier League on May 23. (AFP)
