Slavia equalized thanks to Lukáš Červ who scored from the spot after handplay of one of Barcelona defenders.
The Red Whites came from behind with Daniel Kosek scoring with well-placed shot on 65th minute.
Barca went to ten men after 66 minutes when Sanz hit Červ with his elbow and saw second yellow card. Despite the disadvantage the home side managed to equalize on 85th minute by Mortimer.
But the Red Whites saved their last word for 88th minute when after free kick Adam Toula headed the ball into an open net.
Slavia are now third in Group F with 6 points equal with Borussia Dortmund, 3 points behind Inter.
Tenas - Sergi Rosanas (46. Altimira), Gomes Silva, Medina, Balde (73. Pico), Martinez - Antonio (73. Barri), Sanz, Gonzalez (83. Fernandez) - Jardi (83. Soldevila), Mortimer, De La Fuente
Markovič - Bárta (64. Hošek), Štětka, Vincour, Kosek - Červ, Zinhasovič (90. Vít), Křišťan - Douděra, Toula, Zeronik (30. Felipe)