Wigan Athletic 0 Hull City 1
And Wigan missed the chance to force the tie into extra time when Nigerian international Julius Aghahowa - still without a goal seven months after his £2million arrival - hammered a gilt-edged chance wide.
Wigan, with eight changes to the line-up, had the first chance in a lively opening spell when Kevin Kilbane drilled in an excellent ball from the left and Caleb Folan hit it first time forcing a quality save from Myhill.
Hull responded when Stephen McPhee hammered just wide from around 20 yards and Wigan went close when Henri Camara glanced a header across the face of goal.
Elliott showed his willingness to shoot on sight and Hull threatened again when McPhee's goalbound shot was blocked by Mike Pollitt.
The Latics hit back when David Cotterill picked out Fitz Hall from the corner and the big defender's header was tipped over by Myhill.
But the Tigers took the lead on 31 minutes when Elliott cashed in on a mishit clearance by Andreas Granqvist to volley over the startled Pollitt from 20 yards.
Elliott had the ball in the net again four minutes later, heading past Pollitt at the far post from McPhee's cross but this time he was foiled by an offside flag.
Ex-Fulham midfielder Michael Brown, making his full debut, went desperately close to levelling it with a terrific strike from 25 yards but keeper Myhill flew across goal to force it around the post.
Wigan had an appeal for a penalty turned down when Cotterill went crashing on the edge of the box and Jason Koumas flashed a shot wide.
Aghahowa should have done better after replacing Camara when he was set up by Brown but blasted wide when he had a clear sight of the target with only the keeper to beat.
Hull kept plugging away and substitute Dean Marney almost got a second but headed just over the Wigan bar.