The Czech hosts were always in control of the game at the Generali Arena in Prague and took the lead in the 26th minute.
Tomas Zapotocny found the target for Sparta with a right-footed shot from outside the penalty area.
Four minutes before the half-time interval it became 2-0 to the home side, as Bekim Balaj headed home from close range.
Sparta scored their third goal of the evening in the 56th minute from the penalty spot.
Oscar de Marcos pulled one back for Bilbao on 72 minutes but it was too little too little for the Spanish club, as Sparta bagged maximum points from this Group I contest.