Bradford ended their season with a fifth consecutive win but missed out on the play-offs by a point.
It was an eighth straight defeat for Newport, equalling their worst run since returning to the EFL.
The Exiles had created the better chances in the early stages. Seb Palmer-Houlden had two opportunities to shock the home side but fired one shot over the bar and then screwed another across goal.
Jamie Walker went close for Bradford before they took the lead with a quickfire double just before the break.
Calum Kavanagh nodded home from Brad Halliday’s cross and then Andy Cook claimed his 19th goal of the season when he converted a Richie Smallwood free-kick.
Bobby Pointon made it 3-0 after 56 minutes with a thundering finish into the top corner.
Newport pulled one back through Harry Charsley from Will Evans’ cross.
Matty Platt was denied by a good save from Nick Townsend and substitute Tyler Smith twice went close.
Bradford scored a fourth in stoppage time through Walker but Crawley and Barrow’s results left them in ninth place.
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