Wolves suffered a first-round FA Cup exit following a 2-1 defeat to Oldham in their replay at Molineux.
Oldham memorably knocked Liverpool out in the fourth round last season and made the first steps towards another cup run as Danny Philliskirk (21) and substitute Adam Rooney (73) scored in either half.
Leigh Griffiths pulled a goal back for the League One leaders in injury-time but it was too late to prompt a comeback.
Grimsby upset Scunthorpe 2-1 to claim the bragging rights in north Lincolnshire.
The Mariners are a division below their League Two rivals but led into half-time thanks to Lenell John-Lewis.
Terry Hawkridge levelled a minute after the re-start but Clayton McDonald scored the goal to claim victory, and a second-round meeting with Northampton, on 58 minutes.
Bristol Rovers survived a York comeback to progress 3-2 against their fellow League Two strugglers.
The away side were seemingly cruising when they led 3-0 thanks to goals from John-Joe O'Toole (16), Oliver Norburn (45) and Chris Beardsley (50).
York hit back when Wes Fletcher struck twice in as many minutes, the first a 70th-minute penalty, but that was the extent of their rally.
Wycombe won 2-0 away to Crewe after Steven Craig's 50th-minute penalty was followed by a Gary Doherty strike on 70 minutes.
Robbie Willmott scored the only goal of the game on the stroke of half-time as Newport saw off Braintree while Carlisle also beat non-league opposition as Boreham Wood were defeated 2-1.
Luke Garrard fired the visitors ahead on 29 minutes and an upset looked on the cards when Carlisle gave up another spot-kick two minutes later.
Garrard missed it this time and he was made to pay in the final 10 minutes as Lee Miller and substitute Mark Beck struck.
Bury and Cambridge United drew 0-0 to send their postponed tie to a replay.