Monfils fired 16 aces to set up a clash with sixth-seeded Florian Mayer, who defeated another German, Andreas Beck, 6-4, 3-6, 6-1.
Victor Hanescu rallied to beat Dmitry Tursunov of Russia 3-6, 6-3, 7-6 (7) in two hours, 25 minutes.
The Romanian will next face Brazilian Thomaz Bellucci, who defeated seventh-seeded Lukas Rosol of the Czech Republic 6-4, 6-4. It was Rosol's third consecutive loss.
Nikolay Davydenko of Russia rallied to beat Spain's Daniel Munoz-De La Nava 6-7 (6), 6-3, 6-4.
Also Tuesday, Leonardo Mayer of Argentina rallied to beat Spain's Pablo Andujar 3-6, 7-6 (5), 7-6 (5) over two hours, 55 minutes.
Results from the second day of the Stuttgart Open (x denotes seeded player):
First round:
Thomaz Belluci (BRA) bt Lukas Rosol (CZE x7) 6-4, 6-4
Victor Hanescu (ROM) bt Dimitry Tursunov (RUS) 3-6, 6-3, 7-6 (9/7)
Nikolay Davydenko (RUS) bt Daniel Muoz (ESP) 6-7 (6/8), 6-3, 6-4
Leonardo Mayer (ARG) bt Pablo Andujar (ESP) 3-6, 7-6 (7/5), 7-6 (7/5)
Florian Mayer (GER x6) bt Andreas Beck (GER) 6-4, 3-6, 6-1
Gael Monfils (FRA) bt Paul-Henri Mathieu (FRA) 7-6 (7/0), 6-4