The home side took the lead in the 19th minute when Miroslav Klose was slipped through on goal by Antonio Candreva, and although Francesco Bardi saved his first attempt, he slotted the rebound into an empty net.
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Klose scored his second of the afternoon seven minutes later after collecting a loose ball inside the box and keeping his composure to finish past the keeper.
Paulinho wasted a big chance to bring his side back into the contest, as he fired a shot wide from close range.
After the break, Klose should have sealed his hat-trick when he latched onto a cross and worked space for a shot, but put his effort wide of the post.
Candreva came close scoring a third for Lazio in the final minutes when he worked his way through on goal, but saw his low strike saved by Bardi.