"Barcelona are the best team in the world but anything is possible in football," said Al Sadd coach Jorge Fossati. "If we stay humble and keep this spirit anything can happen."
The Qatari side took the lead against the run of play in Toyota when Khalfan Al Khalfan headed home after a powerful run down the right from Kader Keita in the 33rd minute.
Three minutes into the second half, Doha-based Al Sadd doubled their lead when captain Abdulla Koni swept home a Lee Jung-soo knockdown from point-blank range.
Esperance grabbed a lifeline on the hour mark when skipper Oussama Darragi's flicked headed crept in at the far post but he was furious to be substituted a little over 10 minutes later.
The Tunisians twice had goals ruled offside in a frantic final few minutes but ultimately paid for their wastefulness in front of goal.
Angry Esperance supporters hurled objects onto the pitch while players squared up as tempers boiled over at the end of the game.
Barcelona left for the Far East immediately after beating Real Madrid 3-1 in Saturday's 'Clasico'.
