The Tigers started disastrously as the Hammers hit a quick-fire double through Guillermo Franco and Jack Collison at the KC Stadium.
However, Phil Brown will have been delighted with his side's resilience as the roared back to take a 3-2 lead thanks to a Carlton Cole own goal, a Kamil Zayatte strike and a Jimmy Bullard penalty before the interval.
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The visitors claimed a share of the spoils though after City defender Bernard Mendy had been sent off for a professional foul and they couldn't hold on as Manuel Da Costa fired home the sixth goal of the afternoon.
Brown's men moved outside the relegation places as a result of the draw and have the chance to extend that cushion with another home clash against the Toffees.
David Moyes' men are still struggling with a terrible injury list.
James Vaughan (knee), Leon Osman (ankle), Steven Pienaar, Phil Neville, Victor Anichebe, Phil Jageilka and Mikel Arteta (all knee) are still out of contention as the Merseysiders continue to bemoan their luck.
Hull could be without hamstrung midfielder Seyi Olofinjana while long-term casualty Ian Ashbee (knee) is unlikely to return before the end of the season.
The Tigers will be buoyed by the return of the industrious Bullard, who was in fine form during the weekend draw.
He has only just returned to action after nearly a year on the sidelines but has already shown what he can offer to the team.
Everton slumped to a 3-0 defeat against Manchester United at Old Trafford on Saturday evening as Moyes tinkers with the balance of his side.
They will want to halt their steady slide towards the drop zone as they are now just four points ahead of third bottom Bolton Wanderers.