Harry Kane's first-half penalty gave Tottenham a slender advantage after the Carabao Cup semi-final first leg at Wembley.
Referee Michael Oliver awarded the 26th minute spot-kick after consulting VAR for offside and Chelsea keeper Kepa Arrizabalaga's foul on Kane.
Spurs and Chelsea both had chances in a fiercely fought contest and Blues' manager Maurizio Sarri will feel this tie is still very much alive before the second leg at Stamford Bridge on Thursday, 24 January.
Chelsea hit the woodwork twice in the first half through N'Golo Kante's near-post flick, and when Spurs keeper Paulo Gazzaniga athletically turned Callum Hudson-Odoi's deflected cross onto the post.
Andreas Christensen missed a glaring opportunity from six yards after the break while Arrizabalaga also produced a fine save from Kane as this semi-final remains in the balance.
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Spurs dig deep for victory
This was not Spurs at their fluent, intense best but they showed character and resilience to dig out what may prove to be a decisive advantage as they seek to reach the final for the first time since they were beaten by Chelsea in 2015.
Manager Mauricio Pochettino has made no secret of the fact he does not place this competition high on his list of priorities and would not even regard success in it as a compelling measure of his team's progress - he reserves that status for the Premier League and Champions League.
There is still currency in winning a trophy, however, and success here would go some way towards bolstering Pochettino's reputation as he remains without silverware, for all his good work, and also answer questions about a team that has recently stumbled at the crucial moment.
Kane was the match-winner again as Spurs' chances were limited but they held out at the back as Chelsea increased the tempo after the break, although Sarri's side were also left cursing the woodwork on two occasions.
Barkley fails to shine again
Ross Barkley
Barkley endured a frustrating evening at Wembley
It was, however, a disappointing evening for Ross Barkley who has failed to maintain the early-season form which saw him recalled to the England squad.
Barkley endured a lost season last term - sidelined by a serious hamstring injury in his final months at Everton, then failing to win the faith of former manager Antonio Conte in his early career at Chelsea.
He has had more opportunities this season but the early promise has faded and it was no surprise when he was replaced by Mateo Kovacic with 15 minutes left and Chelsea seeking an equaliser.
Barkley was too often on the periphery of the action; spraying the occasional pass that was pleasing on the eye but too much was safe from a player who won a reputation as a risk-taker.
He is at his best in dangerous areas in and around the goal - an area he was seldom seen, although he did send one shot wildly off target in the first half.
Barkley may be playing to instructions but too much of his game is looking conservative instead of being able to do what he does best: get into attacking positions to make things happen.
No-one can question Barkley's talent but, at 25, he now needs to take the next step and start exerting influence on the important occasions.
It did not happen here and there is no question a player who has been regarded as having outstanding potential for so long must now start to deliver significantly on a regular basis.
Man of the match - Danny Rose (Tottenham)
Danny Rose
Left-back Rose impressed as Tottenham kept another clean sheet, winning the ball back six times, making six clearances as well as contributing two interceptions and one tackle
Spurs keep it tight - the stats
Tottenham have won three successive games against Chelsea in all competitions for the first time since a run of five between March 1961 and September 1963.
Chelsea have lost on each of their last three trips to Wembley, this after losing just three of their previous 11 visits to the stadium (W7, D1, L3).
Chelsea are just the second team to lose twice against the same opponent at Wembley in a single season, after Sheffield Wednesday against Arsenal in 1992-93, who lost the League Cup final and an FA Cup final replay to the Gunners.
Tottenham have kept three consecutive clean sheets in all competitions for the first time since October 2017.
Harry Kane is now the outright fourth highest goalscorer for Tottenham Hotspur, scoring his 160th goal.
Kane has scored in each of his last six games in all competitions for Tottenham, equalling his best streak for the club.
Mauricio Pochettino took charge of his 250th match for Tottenham in this game - his record stands at 143 wins, 53 draws and 54 defeats.
Eden Hazard was fouled on seven occasions against Tottenham; the most fouls he has won in a single game this season - winning seven of Chelsea's 10 free-kicks.
What next?
It's back to Premier League action for both sides at the weekend. Chelsea host Newcastle on Saturday (kick-off 17:30 GMT), while Tottenham welcome Manchester United to Wembley on Sunday (16:30 GMT).
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