Sociedad forward Brais Mendez was shown a straight red card in the 40th minute for a wild challenge on Sergio Busquets.
Barcelona were the better side for most of the match at Camp Nou but only scored once thanks to a brilliant counter-attack by man-of-the-match Dembele in the 52nd minute.
The electric winger ran through the right channel after receiving a perfectly placed long pass from his France team mate Jules Kounde and lashed an unstoppable right-foot strike into the top corner.
In-form Real Sociedad had come to the match with nine consecutive wins in all competitions.
