Clark curled broad for Luton shortly after the restart, however from that second on, it was all Stockport as they went looking for parity.
They went agonisingly near a leveller when the ball dropped for Josh Stokes simply inside the world, however his first-time effort went a matter of millimetres previous the far submit.
Stokes once more almost equalised, with a header on the close to submit from Ollie Norwood’s swinging free-kick – this time he was denied by a superb response save by Shea.
With 10 minutes of stoppages added on, Stockport tried to drive further time, however Luton had different concepts.
Wells received throughout his marker from Shayden Morris’ ball into the field and it fell completely at his ft for him to offer a tidy end to place the sport past doubt.
Addai prevented Luton including gloss to the scoreline, producing a beautiful save at full stretch to his left to cease Gideon Kodua’s goal-bound curling effort, however the harm had very a lot already been carried out.
Victory for Luton means they received the EFL Trophy for the second time, following on from success in 2009, whereas Stockport have now misplaced within the final of this competitors thrice.
Attention will quickly flip to difficult for promotion from League One for each these sides.
But for now, after the highs of the Premier League, adopted by a difficult two years with back-to-back relegations, it’s Luton who can have a good time.