Town had gone into the game top of their group, but defeat by a two goal margin means no possible result in the upcoming fixture between Hull and Grimsby would result in progression to the knockout stage.
Simon Weaver made three changes from Friday night's FA Cup Round One victory as Lloyd Kerry, Aaron Martin and Brendan Kiernan replaced Josh Falkingham, Jack Muldoon and Calvin Miller.
Hull had made ten changes from their fixture at the weekend, but started well forcing Warren Burrell into an early block to divert Hakeeb Adelakun's effort away from goal.
Tom Eaves was looking lively in the Tigers attack, going close with a header before beating Joe Cracknell, though the forward's finish was from an offside position and didn't stand.
After Tom Walker had seen his shot blocked at one end, the tall figure of Eaves had a good opportunity at the other, receiving a cross field pass and bearing down on goal, but Joe Cracknell was able to save with his legs.
Martin Samuelsen twice went close to breaking the deadlock, first heading over at the far post from a Hull corner, then being denied by another fine piece of Cracknell goalkeeping at his near post.
The visitors struck the woodwork with five minutes of the first half to play as Brandon Fleming escaped Kerry and fired at the frame of the goal from a tight angle.
Town's best chance of a half edged by their League One opponents came on the stroke of half time after a patient passing move was worked to Kiernan on the edge of the box, though the winger could only slice wide.
Hull were soon creating chances again after the restart, but again were wasteful as Eaves shot wide from a good position.
Scott was introduced just before the hour mark and almost made an instant impression, going clean through on goal only for Cracknell to extend an arm and claim the ball after the substitute had tried to round him.
The breakthrough arrived 15 minutes from time as Samuelsen swung in a cross from the right that Scott was first to, directing the ball past Cracknell.
Jon Stead, Kevin Lokko and Kiernan all went close to a leveller, but Hull were given the chance to double their lead on 85 minutes as Walker brought down Jones inside the area.
The Hull skipper calmly dispatched the spot kick to seal three points for his side and end Town's hopes of progressing any further in the Papa John's Trophy.
Town: Cracknell, Jones, Burrell, Beck (Thomson 59), Martin (Stead 78), Lawlor, Kiernan, Kirby, Kerry, Walker, Lokko
Subs not used: Belshaw, Falkingham, Muldoon, Miller, Hall
Hull City: Ingram, Batty, Eaves (Chadwick 70), Samuelson, A Jones, Adelakun (Salam 78), Mcloughlin, Slater, Fleming, Mayer (Scott 59), C Jones
Subs not used: Robson, Arthur, Jacob, Hickey
Goals: Scott 75, C Jones 85(p)
Referee: P Wright