The Austrian fourth seed, widely regarded as the man standing between a final showdown between world number one Novak Djokovic and 11-times champion Rafael Nadal, wiped 14th seed Monfils off Court Philippe Chatrier in expeditious fashion.
He will next face either Russian Karen Khachanov or Argentine Juan Martin Del Potro for a place in the last four, where he could meet Serbian Djokovic.
"It was my best match of the tournament so far, some great rallies; it's always fun to play Gael," said Thiem, who advanced in straight sets for the first time this year.
Thiem took full advantage of Monfils misfiring early on to move 4-0 ahead.
It was a necessary cushion as the Frenchman, finally hitting his stride, won four of the five following games. Thiem served for the set at 5-4 and Monfils could offer no resistance.
There was more of a contest in the second set which went on serve until the ninth game, when Monfils hit long to hand his opponent a decisive break.
The Frenchman had no choice but to applaud his opponent after the Austrian hit a winner with a between-the-legs shot after a quick exchange at the net.
Thiem broke for 2-1 but wasted another opportunity in the fifth game. It did not prove costly, however, as Monfils had long lost the thread.
No French woman reached the third round at Roland Garros this year and, in the men's draw, Monfils's defeat followed that of Benoit Paire, who lost focus in a five-set match against Kei Nishikori earlier on Monday.
(Reporting by Julien Pretot; Editing by Clare Fallon)
