Giroud, the league's leading scorer, created Geoffrey Dernis's first-half opener and made it 2-0 just after the break with his 12th goal this season before setting up John Utaka and Remy Cabella to give Montpellier 36 points from 16 games.
"We made it easy for ourselves in the second half by being very efficient," Giroud told Canal Plus TV. "I love to score but if I can create goals for my team mates, that's cool too."
Stade Rennes remained in fourth on 28 points after losing 2-0 at strugglers Nice having played the second half with 10 men following defender John Boye's sending off in the 46th minute.
Second-half substitute Cabella rubbed salt in Lorient's wounds by adding a fourth from a Giroud pass four minutes from time.
Belgian prodigy Hazard started on the bench as Rudi Garcia tried to rest him before next week's decisive Champions League game against Trabzonspor but the Lille coach was forced to send the forward on in the second half with a draw looming.
Aurelien Chedjou's own goal gave Ajaccio an early lead but Lille hit back through Ludovic Obraniak and Marko Basa in the 12th and 16th minutes respectively.
