"I thought she would fight but she doesn't fight," said the 67th-ranked Myskina of her opponent.
"I don't know why she doesn't fight."
The right-handed Myskina, who hits her backhand with both hands, underwent left wrist surgery last November to correct a ligament problem.
The 45-minute match against the 41st-ranked Majoli, the 1997 French Open champion, was the first victory Myskina has posted since rejoining the tour.
She suffered first round defeats in the Ericsson Open and the Boynton Beach satellite.
The top eight seeds, including Swiss Martina Hingis and second seeded Conchita Martinez of Spain received first round byes, and will not play till Wednesday.
In the first set, Myskina won the first eight points to take a 2-0 lead.
Majoli was clearly struggling with her serve and hit double-faults to go down 0-30 and 0-40 in that second game.
Although Majoli was able to recoup the service break in the fifth game of the first set, Myskina won the last three games of the set from 3-3.
Majoli won the first point of the second set and then lost the next 13 points to put Myskina ahead 3-0, 15-0.
Serving in the third game of the second set, Majoli double-faulted on all three points from 0-15 to drop the game.
"I started to fight for every ball," Myskina said. "She knows I can't hit 100 percent (because of my wrist), but I tried my best. She started to make easy mistakes."
Other first round winners on Monday were Dechy, Patty Schnyder of Switzerland, Sandra Cacic of the U.S., and Virginia Ruano Pascual of Spain.