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The closest either side came was when former England ace Nick Barmby fired in a shot from the edge of the six yard box which had to be tipped over the bar by stand-in Blackpool keeper Lee Jones.
At the other end, Boaz Myhill was a virtual spectator for most of the first period as Blackpool strikers Simon Lynch and Scott Taylor struggled to get any change out of big central defenders Damien Delaney and Leon Cort.
The second half started in brighter fashion with Hull creating chances through Delroy Facey and the influential Stuart Green while at the other end a driven shot from Rick Wellens forced Myhill into his first real save.
Fifteen minutes into the half Hull finally found a breakthrough when substitute Danny Allsopp flicked on for the previously anonymous Elliott who scored his first with a powerfully hit drive through a narrow angle.
Blackpool rarely threatened but had a good penalty shout turned down when Lynch hit the ground after a heavy challenge from Delaney but after the state furious protests from Hull players and fans, referee Stuart Mathieson saw nothing wrong and allowed play to go on.
Elliott made the points secure on 84 minutes when another quick break forward gave him the chance to score goal number 21 for the season with another powerful left foot shot.