Barcelona broke the deadlock just before the break, with Sergi Roberto finishing from close range after a winding run from Ferran Torres.
Lewandowski made it two in first-half stoppage time, lashing the ball into the bottom corner from outside the box.
Barca weren't quite as comfortable in the second half, with Cadiz having a goal ruled out and hitting the woodwork twice. Still, the Blaugrana held on to increase their lead atop La Liga to eight points. For now, all focus turns to the second leg of their Europa League clash with Manchester United on Thursday.
GOAL rates Barcelona's players from Camp Nou...