The draw witnessed the pairing of Boro against Spurs, where Mido played for two seasons, in one of the toughest all-Premiership ties.
Another tough encounter will see last season's runners-up Arsenal take on Sam Allardyce's Newcastle at the Emirates Stadium.
Blackburn Rovers will meet Birmingham, Liverpool will visit Reading and Fulham will entertain Bolton.
Holders Chelsea and Premiership champions Manchester United were given relatively easier draws, as the Blues will defend their title at Hull City, while United will host Coventry.
The only game remaining from the second round is the Nottingham Forest vs. Leicester City clash, which was abandoned after the collapse of City's Clive Clarke at half-time.
Third round draw in full:
Blackburn v Birmingham
Reading v Liverpool
Manchester United v Coventry
Tottenham v Middlesbrough
Hull v Chelsea
Blackpool v Southend
West Ham v Plymouth
Arsenal v Newcastle
Luton v Charlton
Manchester City v Norwich
Sheffield United v Morecambe
Sheffield Wednesday v Everton
Fulham v Bolton
Burnley v Portsmouth
Aston Villa v Nottingham Forest or Leicester
West Brom v Cardiff