Hereford were in the Conference last season and Coventry were a perennial Premiership side until recently but that counted for nothing last night as the League Two side trounced Micky Adams' men 3-1.
A hat-trick from 20-year-old Welsh striker Stuart Fleetwood at Edgar Street earned Hereford a place in round two. Dele Adebola scored City's consolation.
One of the other shocks of the night came at Ninian Park, where Dave Jones' Cardiff City were beaten 2-0 by Barnet, thanks to a double from striker Tresor Kandol. As well as the high-flying Bluebirds being beaten, the Eagles - Crystal Palace - had their wings clipped, losing 2-1 at home to Notts County despite going 1-0 ahead through Michael Hughes.
A crowd of just over 10,000 turned up at Elland Road, where a goal from Eirik Bakke earned Leeds United a 1-0 victory over League Two Chester City.
Prolific marksman Freddie Eastwood was on the scoresheet again - he scored twice as Southend won 3-1 at Bournemouth.
A late Ray Jones goal earned Queen's Park Rangers a 3-2 win at home against the courageous Cobblers, Northampton Town.
Journeyman striker Julian Joachim scored the winner as League Two 10-man Darlington recorded a 2-1 upset victory at Championship club Stoke City.
A Joel Porter penalty gave League Two Hartlepool a surprise win at Turf Moor over Steve Cotterill's Burnley, and Championship club Plymouth were beaten 1-0 at home by League Two Walsall.
Derby County and Leicester City both went through, and a late Sebastian Larsson goal gave Birmingham City a 1-0 win against Shrewsbury Town.