The world number seven was in command from the moment he broke serve in the second game.
"I chose to approach the net a lot and that went well for me," Del Potro said. "I needed to do that against Gael who is definitely on his way back.
"It won't take him long before he is battling for a top-10 spot again," added the Argentine, who was beaten 6-1 6-4 by Roger Federer in last year's final in Rotterdam.
Monfils is on the comeback trail after an injury-plagued campaign last season during which he dropped outside the top 100 for the first time since 2005.
"I'm disappointed. Not only because of the defeat but because I had chances in this match," said the Frenchman.
"But overall the body and legs feel great and I know I am improving."
Del Potro now faces Ernests Gulbis after he surprised Robin Haase 6-2 6-1.
Latvian qualifier Gulbis, who has dropped outside the top 100 from a career high of 21, claimed only his second main tour win of the season against the Dutchman.
Russian Mikhail Youzhny sustained a back injury against Dutchman Thiemo de Bakker and had to pull out at 4-1 down in the third and final set.
Roger Federer, the world number two, gets his campaign underway on Wednesday, when he faces Grega Zemlja of Slovenia.
Jo-Wilfried Tsonga was surprisingly beaten in his first-round match on Monday, losing to Dutch wildcard Igor Sijsling.
World Indoor Tournament first round results:
2-Juan Martin Del Potro (Argentina) beat Gael Monfils (France) 6-3 6-4
Jarkko Nieminen (Finland) beat David Goffin (Belgium) 6-0 6-0
Ernests Gulbis (Latvia) beat Robin Haase (Netherlands) 6-2 6-1
Julien Benneteau (France) beat Tobias Kamke (Germany) 6-3 6-2
Thiemo de Bakker (Netherlands) beat Mikhail Youzhny (Russia) 3-6 7-6(2) 4-1 (Youzhny retired)
Brazil Open first round results:
5-Thomaz Bellucci (Brazil) beat Guilherme Clezar (Brazil) 7-6(4) 5-7 7-6(1)
Filippo Volandri (Italy) beat Daniel Gimeno-Traver (Spain) 6-3 3-6 7-6(6)
8-Albert Ramos (Spain) beat Guillermo Garcia-Lopez (Spain) 6-3 7-5
Carlos Berlocq (Argentina) beat Andrey Kuznetsov (Russia) 6-3 6-4
Guido Pella (Argentina) beat 6-Fabio Fognini (Italy) 7-6(6) 1-6 6-1
San Jose Open first round results:
Tim Smyczek (U.S.) beat 5-Fernando Verdasco (Spain) 6-3 6-3
6-Denis Istomin (Uzbekistan) beat Ryan Sweeting (U.S.) 6-3 6-4
7-Marinko Matosevic (Australia) beat Jack Sock (U.S.) 7-6(5) 6-1
Benjamin Becker (Germany) beat Ryan Harrison (U.S.) 6-7(3) 7-5 6-3
Lleyton Hewitt (Australia) beat Blaz Kavcic (Slovenia) 3-6 6-4 7-6(4)
Vasek Pospisil (Canada) beat Evgeny Donskoy (Russia) 7-5 6-1