The German's first goal came from a volley six minutes before half time. A high clearance from the Palermo defense was chased down by Alvaro Gonzalez. Rather than see the ball out for a corner, the Uruguayan turned Santiago Garcia and his right-sided cross was met by the waiting Klose.
Candreva added a stunning second ten minutes after the restart, unleashing a 25 yard shot which looped over the outstretched arm of Samir Ujkani, and beating the Albanian at his near post.
Palermo rarely threatened, but Federico Marchetti did well to parry a Josip Ilicic shot after the Lazio defense made a hash of a clearance in the penalty area.
Klose put the game beyond Palermo seven minutes from the end, chesting down a Senad Lulic cross, before stepping past two defenders and calmly stroking the ball past Ujkani.
It's two wins from two league games now for the Eagles, while it's two heavy defeats in a row for the Sicilians.