The Russian helped get over her Australian Open disappointment by utterly destroying Hantuchova, putting the result beyond doubt within the first half an hour as she won the first eight games in a row.
Her serving in particular was superb - she hit 10 aces in the match - and Sharapova was delighted with her efforts.
"I had a tough first opponent who can play extremely good tennis," she said.
"I wanted to start the match off well. It was extremely important to put that pressure on her from the beginning.
"I think I did that really well today."
WTA Paris results
Anastasia Pavlyuchenkova (Russia) beat 7-Carla Suarez Navarro (Spain) 6-2 3-6 6-3
1-Maria Sharapova (Russia) beat Daniela Hantuchova (Slovakia) 6-0 6-1
Kristina Mladenovic (France) beat 5-Simona Halep (Romania) 7-6(1) 6-4
Galina Voskoboeva (Kazakhstan) beat Stefanie Voegele (Switzerland) 5-7 7-5 7-6(3)
8-Kirsten Flipkens (Belgium) beat Mona Barthel (Germany) 6-3 4-6 6-2
Elina Svitolina (Ukraine) beat 6-Roberta Vinci (Italy) 6-3 0-6 7-5