Swiss forward Innocent Emeghara headed the Tuscans into a sixth-minute lead from Matteo Rubin's cross and the pair combined again to set up Alessandro Rosina for the second midway through the first half.
Emeghara topped off an explosive display with a third after the break.
Lazio were unrecognisable from the side who have again surprised in the upper echelons of Serie A his term and even a change of formation to 4-2-4 failed to inspire the Rome side.
They stay joint-third, level on points with resurgent AC Milan in Italy's final Champions League qualifying spot, having wasted the chance to make up ground on the top two after leaders Juventus lost to AS Roma and Napoli drew with Sampdoria this weekend.
Juve are 11 points above Lazio and Napoli seven after 25 out of 38 matches.
Siena, who started the season with a six-point deduction for match-fixing, rocketed to third from bottom and are now four points adrift of safety after their seventh win of the campaign.
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