Terry Gornell struck just before half-time to send Shrewsbury Town into the FA Cup second round at the expense of hosts Newport County.
A tight encounter was settled when Mark Wright got round his marker on the left wing and sent in a near-post cross that Gornell stooped to head firmly home.
Newport almost equalised, but Craig McAllister's deflected volley was kept out by Chris Neal.
Danny Rose also shaved the post with a curling free-kick but Town held on.
The Shrews had the first sight of goal after 11 minutes when Marvin Morgan robbed Newport left-back Andrew Hughes in the box and brought a smart save from Danny Potter.
In-form Exiles winger Rose's thunderbolt midway through the half might have broken the deadlock, but his well-struck effort went just wide.
The visitors went ahead four minutes before the break when Gornell bagged his second goal in as many games, heading in Wright's whipped near-post cross.
Former Accrington Stanley striker Gornell is reportedly a target for Championship side Leeds and his strike, his fifth of the season, did his chances of a big-money move no harm.
The Exiles thought they had got themselves an equaliser 20 minutes into the second half, but Shrews goalkeeper Neal got a hand to McAllister's volley as it deflected off the back of Wayne Hatswell.
Five minutes later Rose shaved the post with a curling left-foot free-kick as the home side pressed for an equaliser.
But the planned grandstand finish failed to arrive as the Shrews, flying high in League Two, booked their place in the second round against their Blue Square Bet Premier opponents.