A 1-0 win over the League One side, sealed by Harry Kane’s goal, set up a fourth-round tie against Championship club Preston at the end of this month.
A visit to Deepdale will be no gimme for Spurs, who were knocked out last year by second-tier Middlesbrough, but see off another Football League opponent and Conte’s side should be well-placed for a proper Cup run.
Chelsea are out, thrashed 4-0 by Manchester City on Sunday night, and one of Pep Guardiola’s side and table-topping Arsenal will be eliminated after their fourth-round tie, assuming the Gunners beat League One Oxford on Monday.
Liverpool face a tricky third-round replay at Wolves, the winner of which will play Brighton, while Newcastle, Everton, Crystal Palace, Bournemouth, Nottingham Forest and Brentford have also been eliminated.
The draw should give Spurs confidence, but they have not reached an FA Cup Final since winning the competition in 1991, losing eight semi-finals along the way.
Conte, though, led Chelsea to back-to-back finals, winning the second visit in 2018, and for all his grumbling, has a squad capable of beating anyone on their day.
The Italian last week described the Premier League and Champions League as the “best targets”, but has acknowledged that winning either competition is not currently part of his “challenge” at Spurs, raising the possibility that he could come to prioritise the FA Cup.
Winning the competition would further endear Conte to supporters, strengthening his hand in his endless cat-and-mouse negotiations with the club, and potentially sate Kane’s desire for silverware, with the striker’s contract also an increasing priority.
Conte is faced with balancing the need for a top-four finish, which feels essential to Spurs’s business plan and ability to continue to compete in the transfer market, with fans’ desperation to end a 15-year wait for a trophy.
Winning the FA Cup would further endear Conte to supporters, strengthening his hand and potentially sate Kane’s desire for silverware
One positive is an easing injury list, with Rodrigo Bentancur, Dejan Kulusevski and Richarlison all hoping to be in contention to face Arsenal on Sunday, and a new-found confidence in his young players.
Bryan Gil appeared to have no future at Spurs a year ago, but injuries have forced Conte’s hand. After being involved in three of Spurs’s four goals against Crystal Palace on Wednesday, Gil started a third straight game against Pompey and caught the eye with another lively performance.
Conte’s concerns over Gil are not in his technical quality but physique, and the Spain international, 21, has acknowledged that he still has work to do on bulking up but says he has “changed everything” about his conditioning in a bid to win over his manager.
Gil will be in contention to start against Arsenal if Kulusevski or Richarlison do not recover fully in time. Pape Matar Sarr also held his own in his first Spurs start on Saturday, while Oliver Skipp completed his first 90 minutes of the season.
With Conte more willing to trust his youngsters, his squad does not appear as thin as he has suggested, raising the chances of Spurs being able to compete on more than one front.