Merstham will face Oxford United at home when they appear in the first round of the FA Cup for the first time.
The Surrey village team play in the Isthmian League Premier Division, the seventh tier of English football.
Southern League Chesham, also from the seventh tier, face a trip to League One club Peterborough United.
Ninth-tier Westfields will face Curzon Ashton, who upset York City 2-1 in Monday's replay, with ties to be played on the weekend of 5-6 November.
The Midlands League Premier Division club, formed in 1966 following England's World Cup triumph, are the lowest-ranked team left in the competition.
"We are delighted we are at home, six home games on bounce now this season," Westfields chief executive Andy Morris told BBC Sport before the Curzon Ashton result. "I'm quietly confident with a home draw.
"Getting this far is a huge bonus - we have earned enough money so far to get us through this season and keep us going into next season."
Merstham had offered free drinks in their clubhouse from 19:00 BST until their ball, number 79, came up, but the Moatsiders' generosity was presumably shortlived as they were the fourth tie drawn.
Meanwhile, Spennymoor Town of the Northern Premier League will travel to League One MK Dons, while Stamford, who play one level below Spennymoor in the NPL South, will make the trip to Hartlepool if they overcome Wrexham in Tuesday's fourth qualifying round replay in north Wales.
"What an occasion. It is all a reward for the hard work and fantastic opportunity for the supporters to go to the game and hopefully see us win," said Spennymoor manager Jason Ainsley.
A total of 39 non-league clubs joined the 48 from Leagues One and Two in the first-round draw, with the winners of seven ties still to be decided following draws on Saturday.
Bolton Wanderers and Sheffield United, both four-time cup winners, face home ties against Leyton Orient and Grimsby Town respectively.
National League Altrincham - who beat Barnsley at the same stage last season - take on either Lincoln City or Guiseley.
Meanwhile, 2008 winners Portsmouth will be at home to League Two rivals Wycombe Wanderers.
Premier League and Championship clubs will enter the competition at the third-round stage.
Full FA Cup first-round draw:
Sheffield United v Leyton Orient
Millwall v Southend United
Dagenham & Redbridge v FC Halifax Town
Merstham v Oxford United
Taunton/Hemel Hempstead v Barrow
Southport v Fleetwood Town
Yeovil v Solihull Moors
Stockport County v Torquay/Woking
Dartford v Sutton United
Walsall v Macclesfield Town
Port Vale v Stevenage
Northampton v Harrow Borough/Margate
Cambridge United v Dover Athletic
Westfields v Curzon Ashton
MK Dons v Spennymoor Town
Gillingham v Brackley Town
Alfreton/Gateshead v Newport County
Portsmouth v Wycombe Wanderers
Maidstone United v Rochdale
Bury v AFC Wimbledon
St Albans City v Carlisle United
Boreham Wood v Notts County
Mansfield Town v Plymouth Argyle
Braintree Town v Eastbourne Borough
Hartlepool United v Wrexham/Stamford
Bolton Wanderers v Grimsby Town
Bradford City v Accrington Stanley
Oldham Athletic v Doncaster Rovers
Eastleigh v Swindon Town
Shrewsbury Town v Barnet
Morecambe v Coventry City
Crawley Town v Bristol Rovers
Whitehawk v Stourbridge
Colchester United v Chesterfield
Lincoln City/Guiseley v Altrincham
Exeter City v Luton Town
Charlton Athletic v Scunthorpe United
Cheltenham Town v Crewe Alexandra
Peterborough United v Chesham
Blackpool v Kidderminster Harriers