Yeovil took the lead through Marcus Stewart in the 25th minute but Todd and Stevens turned the game on its head before the break and sealed victory with further goals after the interval.
Rotherham avoided similar embarrassment as Chris O’Grady’s 84th-minute equaliser earned a 2-2 draw at Forest Green. There was no fairytale at Gainsborough, who were thrashed 6-0 by Hartlepool.
On Saturday, Blue Square North side Barrow earned a first-round replay against League One Bournemouth after a 1-1 draw at Holker Street. Kevin Rapley put the Cumbrian side ahead after 19 minutes but any hopes of killing off the Cherries at the first attempt were dashed by Jem Karacan’s equaliser.
Billericay Town, from the Isthmian League Premier Division, came within seven minutes of earning a replay against League One Swansea. Wayne Semanshia had given the Essex side an unlikely lead but a brace from City striker Guillem Bauza put the visitors through to the second round.
Mo Harkin’s goal sent Havant and Waterlooville into the second round for the first time in their history at the expense of Blue Square Premier side York at KitKat Crescent. The former Northern Ireland U21 international netted midway through the first half.
Marc Charles-Smith’s 76th-minute goal gained Staines Town a replay against Stockport, who had taken the lead through Matthew McNeil.
Huddersfield came from two down at half time to beat Accrington Stanley 3-2 at the Fraser Eagle Stadium. Peter Cavanagh and Paul Mullin put the hosts into a comfortable lead after 25 minutes but the Terriers bounced back with a brace from Malvin Kamara and a late strike from Luke Beckett.
Millwall, the 2004 finalists, came from a goal behind against Altrincham to secure a 2-1 win.
Two goals each for Daryl Clare and John McGrath helped Burton Albion beat Halifax at The Shay, while Peterborough saw off League Two strugglers Wrexham 4-1.
Non-league sides Chasetown, Harrogate Railway and Horsham all booked their places in the draw for the second round with wins over Team Bath, Droylsden and Maidenhead United respectively.
Second round draw: Oxford Utd v Southend, Swindon v Forest Green/ Rotherham, Oldham/ Doncaster v Crewe, Darlington/ Northampton v Walsall, Cambridge Utd v Weymouth, Millwall v Barrow/ Bournemouth, Stockport/ Staines v Peterborough, Bradford v Tranmere, Torquay v Cheltenham/ Brighton, Notts County v Havant and W, Dag & Red v Kidderminster, Port Vale v Chasetown, Leyton Orient/ Bristol Rovers v Rushden & Diamonds, Huddersfield v Carlisle/ Grimsby, Burton v Barnet, Bury v Exeter, Luton/ Brentford v Lincoln / Nottm Forest, Horsham v Swansea, Hereford/ Leeds v Hartlepool, Harrogate Railway v Mansfield.
Matches to be played 1-2 December.