Balde Keita opened the scoring at Torino's Stadio Olimpico with a well-taken finish from a tight angle in the 13th minute.
Veteran striker Miroslav Klose put the Rome club 2-0 up just shy of the half-hour mark when he showed his predatory instincts to meet Danilo Cataldi's centre.
Josef Martinez gave Torino hope shortly after the break when he sprung the offside trap and lashed home to reduce the arrears.
However, Giampiero Ventura's side were hindered when goalkeeper Daniele Padelli brought Klose crashing to ground in the area, prompting a red card and a penalty for Lazio in the 57th minute.
Cristian Ledesma made no mistake from the spot as Lazio progressed to face Milan in the last eight.
In Wednesday's other last-16 tie, Parma defeated fellow Serie A strugglers Cagliari 2-1 at the Stadio Tardini.
Gabriel Paletta put the hosts into the lead on the stroke of half-time, only for Cagliari to restore parity through Marco Sau.
Parma won the match with just six minutes remaining, though, thanks to defender Andrea Rispoli's strike.
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