It was a slow start for the Spanish world number five, but she eventually worked her way into the contest, growing in confidence as the game progressed to set up a third-round match against Yulia Putintseva.
"I think I was a little bit nervous when I started off, because I knew she was going to be a tough opponent. She was very quiet, very relaxed, and I had to calm down."
"So it took me a while to get things back under control," said the 23-year-old, who was beaten by the Estonian in Stuttgart just last month.
The Spaniard looked in real trouble when Kontaveit, ranked 53rd in the world and in stellar form that has seen her reach the final in Biel and the quarter-finals in Rome, took a one-set and 2-0 lead.
Muguruza was kept in the contest by her serve, winning 72 percent of all her first service points.
"In all of these long rallies, it's really important to have a robust serve, to have a little more robustness and don't rush things," she said.
She needed just over two hours to overcome Kontaveit, who by that time had run out of steam, slapping a backhand wide.
"I refused to feel I was being defeated. I knew I could turn things around. I knew that if I insisted with my strategy I could succeed," Muguruza said.
(Reporting by Karolos Grohmann; Editing by Alison Williams and Hugh Lawson)
