The third-seeded Russian and defending champion broke Duque-Marino's serve four times while saving three break points on her own serve.
"She is someone who, if you give her time, creates angles, slices and usually drop-shots a lot more than she did in this match because she has the hands and the ability to do so," Sharapova said.
Sharapova's next opponent will be Caroline Garcia of France, who beat the 14th-seeded Karolina Pliskova of the Czech Republic 6-2, 4-6, 6-1.
Fourth-seeded Petra Kvitova of the Czech Republic also advanced, beating Coco Vandeweghe of the United States 6-4, 2-6, 6-3.
Also, Barbora Strycova of the Czech Republic beat Varvara Lepchenko of the United States 6-4, 6-2, and Victoria Azarenka of Belarus defeated Ajla Tomljanovic of Croatia 6-3, 6-3.
Azarenka's next rival is the top-seeded Serena Williams.
Anastasia Pavlyuchenkova of Russia rallied in a hard-fought second set to beat Sara Errani of Italy 3-6, 7-6 (7), 6-4.
In the men's tournament, fifth-seeded Milos Raonic of Canada served nine aces and broke Argentine player Juan Monaco's serve twice to win 6-3, 6-4.
Also, 10th-seeded Grigor Dimitrov of Bulgaria advanced after Donald Young of the United States had to retire from the match because of injury.
The 25-year-old Young received treatment for back pain while trailing 6-4, 3-0 and was unable to resume play.
Dimitrov will next face Fabio Fognini of Italy.
Fernando Verdasco, who lives in Madrid, beat fellow Spaniard Guillermo Garcia-Lopez 4-6, 6-2, 6-3.
Leonardo Mayer of Argentina beat Gilles Muller of Luxembourg 6-3, 6-3.
Also advancing were Jo-Wilfred Tsonga, Gael Monfils and Alberto Ramos-Vinolas.