Diego Costa's first top-flight goal this season looked set to give Diego Simeone his maiden league victory against Barcelona in seven years as Atletico's head coach, which would have taken them to the summit.
But it was not to be as Dembele found space in the box in the last minute to beat Jan Oblak with a low shot that evaded a desperate effort by Lucas Hernandez to clear the ball off the line.
A draw maintains the status quo at the top of LaLiga with Barca a point clear of Atletico having successfully avoided suffering back-to-back league losses for the first time under Ernesto Valverde.
Thomas Lemar fired an early effort off target but Barca had to wait until the 40th minute for their first shot, Lionel Messi blazing a free-kick over the crossbar after Lucas fouled him.
Barca lost Sergi Roberto to injury at half-time and both sides continued to struggle to create chances after the interval.
Atletico appealed for a penalty when the ball appeared to strike Arturo Vidal on the arm, but VAR ruled no offence had been committed.
But they did edge ahead with 13 minutes to go, Costa producing a towering header from Antoine Griezmann's right-wing corner – Atletico's first of the game – to open his account in style, sparking wild celebrations at the Wanda Metropolitano.
Messi's free-kick earned Barca a 1-0 win over Atletico in March that effectively ended the title race last term, but he could not repeat the trick as he hit a set-piece straight at Jan Oblak.
However, the Barca captain set up his side's dramatic late equaliser, carving open the Atletico defence for the first time by feeding late substitute Dembele on the right of the penalty area.
The France forward cut inside onto his left foot and beat Oblak and Hernandez to keep Barca top of LaLiga.
What does it mean? Barca miss chance to stretch lead
Diego Godin's absence handed Barcelona an opportunity to move clear at the top, but Ernesto Valverde's men were successfully stifled by Atletico until Dembele's late impact. Atletico's hopes of a first title since 2013-14 appeared set to be given huge boost by Costa's superb headed goal but instead they will rue two dropped points that could be crucial in May.
Dembele writes positive headlines
It is fair to say Dembele has not settled at Barcelona, with regular speculation about his private life and future, while his poor timekeeping has irked Valverde. The Barca coach only turned to the former Borussia Dortmund star after Costa's header but he showed his value.
Vidal display shows Rakitic importance
With Ivan Rakitic sitting the game out due to suspension after his red card against Real Betis last time out, Vidal was given a chance to shine in midfield. However, the Chile international toiled in the face of Atletico's ferocious pressing and could have conceded a penalty for what appeared to be a handball.