Leeds had to settle for a point after coming from behind to take the lead only to concede against ten men late on.
Simon Grayson made three changes from the side that beat Coventry City on Saturday.
In came Kasper Schmeichel, Alex Bruce and Bradley Johnson in place of Jason Brown, Amdy Faye and Neil Collins.
Leeds made a fast start; Snodgrass had a good run down the right that Becchio failed to control in the middle and that allowed the Hull defender Ayala time to clear.
Hull took the lead on the quarter owith their first meaningful effort when John Bostock gave Schmeichel no chance with a long distance free kick.
The goal stunned Leeds and they had to wait almost ten minutes for their first chance but Max Gradel shot well over.
Leeds were beginning to find their composure again, Howson shot wide after being set up by Becchio.
Johnson tried to chip Matt Duke, but it was easy for the Hull keeper.
Johnson did get on the score sheet soon after when he nipped in to strike his shot hard and low to give Duke no chance.
Hull almost took the lead again within minutes when Bostock saw his shot cleared off the line by Bruce and go out for a corner.
From the resulting corner, Dawson missed a great chance with a header that hit a Leeds defender with the visitors claiming handball.
Snodgrass then saw his header from a Gradel free kick go over the bar.
Leeds then had strong claims for a penalty waved away when Ian Ashbee handled in the area.
Leeds started the second half strongly, Howson saw his shot from a tight angle hit the side netting and Becchio had the best early chance when his shot hit the crossbar.
Becchio then had another chance but this time his header went well wide from a Snodgrass cross.
Simon Grayson made his first substitution halfway through the half when Davide Somma replaced Max Gradel.
Leeds took the lead soon afterwards a ball into the middle found Andy O`Brien and his effort went in off the post.
The goal was thoroughly deserved as Leeds had dominated the second half.
Leeds almost made it three within minutes when Bradley Johnson headed just wide from a corner.
The evening got worse for Hull when Paul Bostock was sent off for a second bookable offence for a challenge from behind.
Despite going down to ten men, Hull got back on level terms when Bradley Johnson sliced the ball into his own net from a Hull corner with just eight minutes remaining.
Simon Grayson quickly made his second substitution of the evening when Lloyd Sam replaced Kilkenny.
Leeds almost retook the lead when Bruce saw his header cleared off the line in the final minute of normal time.
Billy Paynter came on for the final exchanges when he replaced Luciano Becchio in attack with four minutes of ‘Fergie time` remaining.
Despite the added time Leeds couldn`t find a winner and will be disappointed to have dropped two points in a game they dominated for long periods.
Schmeichel, Connolly, O`Brien, Bruce, McCartney, Howson, Snodgrass, Johnson, Kilkenny (Sam 88), Becchio (Paynter 90), Gradel (Somma 68)
Subs not used
Brown, Hughes, Collins, Nunez,
Duke, Zayette, (Cairney 69), Rosenior, Gerrard, Dawson, Ayala, Kilbane (Cullen 81), Ashbee, Harper, Garcia, Bostock
Subs not used
Solano, Mannone, Halmosi, Cooper, Simpson
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