Sean Newton's penalty gave Telford all three points against a visiting Newport side who had two men sent off.
Richard Davies put the Bucks ahead from the edge of the area after Dwayne Samuels' cross was only half-cleared.
County equalised through Danny Rose's fine 30-yard free-kick, but Newton restored Telford's lead when Gary Warren fouled Andy Brown in the area.
Newport's Scott Rogers was sent off for a lunge on Samuels before Tommy Doherty earned a second yellow for dissent.
AFC Telford: Young, Salmon, Killock (Whitehead 46), Preston, Newton, Samuels, Davies, Trainer, Valentine, Mills, Brown (Farrell 67). Subs Not Used: Lee Evans, Rooney, Meechan.
Booked: Mills, Valentine.
Goals: Davies 17,Newton 57 pen.
Newport County: Potter (Thompson 40), Rodgers (Rogers 74), Warren, Yakubu, Hughes, Rose, Miller, Doherty, Jardim (Foley 39), McAllister, Buchanan. Subs Not Used: Baker, Velez.
Sent Off: Rogers (88), Doherty (90).
Booked: Potter, Miller, Warren, Foley, Doherty, Yakubu.
Goals: Rose 41.
Ref: Peter Banks (Merseyside).