Elsewhere, holders Chelsea face a trip to Deepdale to take on Championship side Preston.
Arsenal, who came from behind to defeat West Ham 2-1 at Upton Park, face another trip to Premier League opposition - Stoke.
Manchester City travel to Championship side Scunthorpe, Aston Villa take on League One Brighton, while Championship rivals Southampton and Ipswich meet in the only other confirmed ties.
Liverpool will have a home meeting against Burnley if they win their replay against Reading, while last year's beaten finalists Everton await the winner of Nottingham Forest's replay against Birmingham.
Managerless Bolton welcome either Sheffield United or QPR to the Reebok Stadium, while Sunderland - safely into the last 32 after the 3-0 home win over non-league Barrow - travel to Portsmouth or Coventry.
Fulham must face the winners of Accrington's tie against Gillingham, while Wigan go to either Notts County or Forest Green - the last non-league team left in the draw.
Wolves have a home contest against Crystal Palace.
West Brom will play Plymouth or Newcastle, while another all-Championship affair sees Bristol City or Cardiff face Leicester.
The other tie sees Millwall or Derby, who must replay at Pride Park, take on Brentford or Doncaster - who were denied by the weather on Saturday.
Grayson was not getting too carried away with the prospect of another Premier League scalp after Leeds were drawn to face Spurs at White Hart Lane.
"We have a long season in terms of games but hopefully a successful one as well," the Leeds manager told Sky Sports News.
"It's a good draw again. We're up against a top Premiership team and a top manager and we'll approach that as we have done for the Manchester United game - with the respect that they deserve.
"But we've got a few league games in between and that's our bread and butter.
"It's another fantastic draw and another game that could have been quite easily a Premier League fixture five or six years ago."
Brighton boss Gus Poyet, who was part of the Chelsea team which beat Aston Villa 1-0 in the 2000 FA Cup final at Wembley, was thrilled by the thought of a trip to Villa Park.
"All the players and club and fans are very excited about it," he said.
"It's going to be one of the big ones. The club are looking forward to the game.
"It's going to be tough but it's important for the players to have the opportunity to play against Aston villa.
"Everyone at the club, I have to say, they wanted to play away against a Premiership club so I think it's perfect for everyone."
Fourth-round draw in full:
Southampton v Ipswich, Reading/Liverpool v Burnley, Millwall/Derby v Brentford/Doncaster, Bristol City/Cardiff v Leicester, Stoke v Arsenal, Notts County/Forest Green v Wigan, Scunthorpe v Man City, West Brom v Plymouth/Newcastle, Everton v Nottm Forest/Birmingham, Accrington/Gillingham v Fulham, Bolton v Sheff Utd/QPR, Portsmouth/Coventry v Sunderland, Preston v Chelsea, Aston Villa v Brighton, Tranmere/Wolves v Crystal Palace, Tottenham v Leeds.