World number 19 Hantuchova breezed past Columbia's Catalina Castano 6-1 6-0 in 53 minutes while Schiavone, ranked 25, downed Bulgarian Tsvetana Pironkova 6-2 6-4 in one hour 26 minutes.
Mirza overcame early hiccups to defeat Italy's Romina Oprandi 6-4 6-3 while Santangelo edged past German wild card Sandra Kloesel 6-3 7-6.
Mirza, who has had a good start to the season, started off slowly and trailed Oprandi early in the first set.
But she began to play some excellent forehands, often passing Oprandi with clinical precision, to gain the advantage.
As the match progressed, Mirza showed a lot of improvement on her serve, and managed to break Oprandi twice in the first set and three times in the second.
"I've had some starting trouble, but it was important to get through the first round," said Mirza.
Hantuchova seemed to be in a hurry as she demolished Castano with a flurry of shots.
Schiavone took a while to find her rhythm but once she settled down to a pattern, returning well from the baseline, she proved too good and Pironkova had to play second fiddle.
The Italian broke her opponent twice to clinch the first set and continued her dominance in the second too, playing some exquisite shots from the back of the court.
Pironkova showed flashes of brilliance, breaking Schiavone twice, but the Italian replied with three breakpoints to wrap up the match without much troubled.
Schiavone, who lost her first round match in Dubai last week to Patty Schnyder of Switzerland, said she was happy to have progressed into the second round.
"I am quite happy to get off to a win. It was not that easy, there were some challenges," she told reporters.
Italy's Mara Santangelo was the other first round winners on Monday.
Belgian Justine Henin, Russia's Svetlana Kuznetsova, Switzerland's Martina Hingis and Serbia's Jelena Jankovic are the top four seeds in the tournament.
