The top seed advanced into the Roland Garros last eight with a 6-1, 6-2, 6-3 triumph over Richard Gasquet (FRA, 20) in two hours.
Top seed defeated rising Australian teenager Thanasi Kokkinakis in straight sets to reach the fourth round of the French Open for a ninth time.
Novak beat 55th-ranked Gilles Muller of Luxemburg 6-1, 6-4, 6-4 for a place in the third round of the 2015 Roland Garros.
Novak began his quest for a first Roland Garros crown with a 6-2, 7-5, 6-2 victory over 87th-ranked Jarkko Nieminen on Tuesday.
The second Grand Slam of the season, the Roland Garros, is taking place in Paris, from May 24 to June 7, 2015.
Novak won his fourth Internazionali BNL d’Italia crown with a 6-4, 6-3 victory over second seed Roger Federer on Sunday.
Novak will contest his sixth final at Foro Italico on Sunday (16:00 CET) when he meets no.2 seed Roger Federer.
Defending champion advanced to his sixth semi-final in Rome as he beat no.5 seed Kei Nishikori 6-3, 3-6, 6-1 on Friday.
Nole rallied from a set down to defeat Thomaz Bellucci 5-7, 6-2, 6-3 on Thursday and reach the quarter-finals at Foro Italico.
Top seed and defending champion beat Nicolas Almagro 6-1, 6-7 (5), 6-3 to reach the last 16 at the Internazionali BNL d’Italia on Tuesday.