Dembele has become an unpopular figure with Barca fans after failing to agree an extension to his contract, which expires at the end of the season, but his thunderous effort six minutes after arriving from the bench made sure of a Camp Nou victory.
After Atletico Madrid had leapfrogged the Blaugrana with its win on Sunday (AEDT), Pierre-Emerick Aubameyang continued his fine recent scoring form to set Xavi's side on its way, before Dembele struck and then twice crossed for Luuk de Jong and the fit-again Memphis Depay in the closing stages.
With Real Betis beaten by rival Sevilla, Barca is now just a point behind third place with a game in hand as its season maintains an upwards trajectory.
Gerard Pique saw a header cleared on the line by Oier Zarraga while Ferran Torres tested Unai Simon with a stinging volley as Barca dominated the opening exchanges.
The reward for Xavi's host arrived on 37 minutes when Aubameyang acrobatically finished after Pique headed against the crossbar from Dani Alves' corner.
Torres should have doubled his side's advantage past the hour mark, but his tame effort was pushed away by the onrushing Simon, who then denied Aubameyang's weak header.
Simon was powerless to stop Dembele, though, as substitute Frenkie de Jong found the winger, who smashed a left-footed attempt in from the left side of the box, earning a touch off the post as he put the game beyond doubt.
There was still time for Luuk de Jong to flick a header into the bottom-left corner after Dembele's pinpoint delivery from the right, before the France international repeated the trick to find Depay, who turned in from close range for the final goal.