It looked like being a familiar story for the 31-year-old when 11th seed Querrey bombed down nine aces to win the opening set, but crowd-pleaser Monfils responded with some dazzling tennis to win 5-7 6-4 6-4 6-2 on Centre Court.
Monfils levelled the match with an ace of his own after breaking for a 5-3 lead in the second set.
A forehand pass gave him the breakthrough midway through the third set and Querrey's resistance faded in the heat as Monfils raced through the fourth in 23 minutes.
He will face South African eighth seed Kevin Anderson next.
"It's taken a long time for sure," Monfils said. "Years and years. I had to put myself in a good opportunity, to put myself in a good balance with my body and my belief on a grass court.
"The last three years were much better. I just couldn't take the opportunity. Today I took it and I'm happy about it."
(Reporting by Martyn Herman; editing by Clare Fallon and Ken Ferris)
