Evian, 17th in the French top flight, bolstered their chances of finishing outside the relegation zone come the end of the campaign thanks to a 1-0 win over Guingamp, with Cedric Cambon on target.
Majeed Waris scored the winner at the Stade du Roudourou as Valenciennes, the side immediately below Evian, registered a 2-1 win against 10-man Rennes.
Ola Toivonen opened the scoring for Rennes but Mathieu Dossevi levelled before Waris followed up his 75th-minute penalty, awarded following a foul that saw Jean-Armel Kana-Biyik sent off, to score at the second attempt and turn the tide for Ariel Jacobs' side.
Despite Edouard Butin's reply, Monaco held on - aided by the late dismissal of Jordan Ayew - and moved 10 points clear of third-placed Lille.
Rene Girard's side face Montpellier on Sunday and will know that victory is imperative if they are to keep their faint hopes of an automatic UEFA Champions League spot alive.
Lavezzi added a third goal two minutes from time to wrap up an enjoyable afternoon for Laurent Blanc, although Monaco's subsequent success against Sochaux ensured PSG's lead at the summit remains eight points.
