Arsenal's most recent piece of silverware came in the 2005 FA Cup but if they are to repeat that success this season they will have to overcome Spurs at the first hurdle after the two sides were paired together in the pick of Sunday's draw.
The pair are among the most successful clubs in the competition's history, with Arsenal having lifted the trophy on 10 occasions while Spurs have won it eight times.
The only side to have won the FA Cup more times are Manchester United, who will also be involved in an all-Premier League tie in the third round after being paired at home to Swansea.
United might have been hoping for a more favourable cup draw following a hugely disappointing start to the defence of their league title which has seen them lose five times in 15 matches under new boss David Moyes, with their latest setback Saturday's 1-0 loss to Newcastle at Old Trafford.
United have won the FA Cup 11 times, but the last time was back in 2004.
FA Cup holders Wigan start off against MK Dons while the side they beat in May's final, Manchester City, face a short trip to Blackburn.
Liverpool, who moved up to second in the Premier League standings with their 4-1 win over West Ham on Saturday, could face Oldham in their third-round tie - the team that knocked them out last season.
Oldham beat the Reds 3-2 in the fourth round and they will get another crack at Brendan Rodgers' men if they can overcome Mansfield in their second-round replay.
Liverpool also met Mansfield in the third round last season, with Luis Suarez's contentious second goal - when the Uruguay international handled the ball before scoring - earning his side a 2-1 win.
There are a number of other all-Premier League ties, with in-form Newcastle hosting Cardiff, Norwich taking on Fulham and Crystal Palace going to West Brom
The top three sides in the Sky Bet Championship, meanwhile, are all away to top-flight opposition with leaders Burnley at Southampton, second-placed QPR going to Everton and Leicester in third taking on Stoke.
Steve McClaren's Derby, who are up to fourth in the second tier after winning their last five matches, were handed a home time against a Chelsea side looking to win the cup for a fifth time in eight seasons
Nottingham Forest, fifth in the Championship, will also need to claim a Premier League scalp if they are to reach the fourth round after being drawn at home to West Ham.
In ties involving the other top-flight teams, Aston Villa take on Sheffield United, Middlesbrough meet Hull while rock-bottom Sunderland host Carlisle.
Of the non-league clubs still involved in the competition, Kidderminster were drawn against Peterborough, Grimsby face Huddersfield while Macclesfield are up against Sheffield Wednesday.
Another conference side, Wrexham, will go to Charlton if they can overcome League Two pacesetters Oxford in their second-round replay.
In other games, last season's semi-finalists Millwall are at Southend, Brighton welcome Reading, Bolton take on Blackpool, League One leaders Leyton Orient go to Yeovil, Rochdale face Leeds, Ipswich clash with Preston, Bristol City take on Watford, Doncaster face Stevenage and Plymouth go to Port Vale.
Also, Barnsley host Hartlepool or Coventry, Birmingham meet Bristol Rovers or Crawley while Bournemouth take on Fleetwood or Burton.
FA Cup third round draw:
Barnsley v Hartlepool/Coventry
Yeovil v Leyton Orient
Liverpool v Oldham/Mansfield
Nottm Forest v West Ham
Bristol City v Watford
Southend v Millwall
Middlesbrough v Hull
West Brom v Crystal Palace
Kidderminster v Peterborough
Doncaster v Stevenage
Stoke v Leicester
Southampton v Burnley
Newcastle v Cardiff
Rochdale v Leeds
Wigan v MK Dons.
Charlton v Wrexham/Oxford.
Man Utd v Swansea
Port Vale v Plymouth
Norwich v Fulham
Aston Villa v Sheff Utd.
Macclesfield v Sheff Wed.
Sunderland v Carlisle.
Bolton v Blackpool
Blackburn v Man City
Everton v QPR
Brighton v Reading
Arsenal v Tottenham
Birmingham v Bristol Rovers/Crawley
Grimsby v Huddersfield
Ipswich v Preston
Derby v Chelsea
Bournemouth v Fleetwood/Burton
Matches to be played over the weekend of January 4-5.