The pair locked horns at the Keepmoat Stadium at the start of the 2012-13 campaign, with the Minstermen agonisingly losing out on penalties after the tie ended 1-1 after extra time.
This time around, the pair meet at Bootham Crescent, with York crashing at the first-round stage on home soil last season in a 4-0 home reverse to Burnley.
York has not proved a happoy hunting ground for Rovers over the years and the South Yorkshire outfit have not won in their past nine outings at Bootham Crescent.
Their last victory arrived way back on Boxing Day 1985.
Elsewhere, Leeds United have been handed a home encounter with James Beattie’s Accrington Stanley, the fifth successive year the Whites have been afforded home advantage in round one, having previously played Chesterfield, Shrewsbury, Bradford City and Lincoln City.
Meanwhile, the Steel City duo of Sheffield Wednesday and Sheffield United have also been handed home ties against Notts duo Notts County and Mansfield Town respectively.
Middlesbrough visit Oldham, with Boundary Park a bogey ground for the Teessiders over the years.
Bradford City, beaten finalists in 2012-13, head over the Pennines to Morecambe.
Meanwhile, Huddersfield Town face a reunion with former winger Gary Roberts, having been handed an opening round trip to Chesterfield.
Steve Evans’ Rotherham United host Fleetwood, who knocked them out of the Johnstone’s Paint Trophy at Highbury Stadium last term.
The tie sees Ryan Cresswell and Gareth Evans face their former employers.
Barnsley entertain Crewe. Ties to be played on the week beginning August 11.
Full draw: Oldham v Middlesbrough; Shrewsbury v Blackpool; Sheffield Wednesday v Notts County; Tranmere v Nottingham Forest; Leeds v Accrington; Bolton v Bury; Rochdale v Preston; Rotherham v Fleetwood; Carlisle v Derby; Port Vale v Hartlepool; Morecambe v Bradford; Barnsley v Crewe; Chesterfield v Huddersfield; Blackburn v Scunthorpe; Burton Albion v Wigan Athletic; York v Doncaster; Sheffield United v Mansfield; Reading v Newport; Bristol City v Oxford; Brighton v Cheltenham; Coventry v Cardiff; Luton v Swindon; Dagenham & Redbridge v Brentford; Charlton v Colchester; Crawley v Ipswich; Wolves v Northampton; Yeovil v Gillingham; MK Dons v AFC Wimbledon; Exeter v Bournemouth; Stevenage v Watford; Plymouth v Leyton Orient; Birmingham v Cambridge; Portsmouth v Peterborough; Millwall v Wycombe; Southend v Walsall.