Brayan Perea put the Italians on their way in the 24th minute before Felipe Anderson doubled his team's lead before the hour mark.
Legia proved no threat for the Romans, who secured their third win in the competition.
The outcome allowed Lazio to join Group J leaders Trabzonspor in the next round while for Legia the misery continued as this defeat made it five losses from five in the group.
Lazio are seven points clear of third-placed Apollon Limassol, who lost 4-2 in Turkey, and three points adrift of Trabzonspor.
The Italians take on Trabzonspor in Rome on December 12 in a battle for top spot while Legia end the competition against Apollon.
Lazio dominated possession and had the first chance in the 18th minute when Luis Cavanda's strike from just outside the area was kept out by Legia Warsaw goalkeeper Dusan Kuciak.
Lazio went ahead shortly after.
There was nothing Kuciak could do after Perea headed Lucas Biglia's cross into the very corner of the net.
The hosts could have restored parity two minutes later but Vladimer Dvalishvili nodded narrowly over the bar.
Lazio increased the tempo and twice had the chance to extend their advantage before the interval.
Kuciak punched away Keita's bullet strike from 30 yards before Alvaro Gonzalez headed Stefan Radu's cross wide.
The Italians continued to press forward after the break and were rewarded in the 57th minute.
Hernanes fed Felipe Anderson in the box and his right-footed shot from 18 yards beat Kuciak.
The Poles should have reduced the deficit on 67 minutes but substitute Henrik Ojamaa missed an open goal when he fired wide after Lazio goalkeeper Etrit Berisha had come off his line.