Wildcard entrant Sharapova, a five-time Grand Slam winner, returned to action only this week following her 15-month drugs ban, but has looked like she never really went away in winning her three matches so far without dropping a set.
Sharapova has also received wildcards for upcoming tournaments in Madrid and Rome, angering some players who say a doping offender should start from the lower-tier tournaments and earn back ranking points instead.
Reaching the Stuttgart final could be enough to move Sharapova's ranking back above 200 and secure her a spot in the qualifying tournament for the French Open, and if she did well in Madrid and Rome she might make the main draw for Wimbledon.
"I thought I had a really good rhythm today," Sharapova told reporters. "When you don't know your opponent too well you try to figure them out and when I got my opportunity I took it," she said of her dominant phase late in the first set.
"It's part of being a competitor. We work too hard to come out here and not to give it everything we have. It's important to have that intensity."
The 21-year-old Kontaveit, who battled through the Stuttgart qualifiers into the main draw, confirmed her fine current form early in Friday's match, comfortably holding serve and matching Sharapova's power from the baseline.
The Estonian world number 76, fresh from her first WTA tour final earlier this month, was broken twice in a row though as Sharapova upped the pressure, attacking every serve of her opponent to win five games in a row.
Sharapova broke again early in the second set and despite twice dropping her serve in a late bout of nerves she broke the Estonian again, sealing victory on the first match point as Kontaveit sent a forehand long.
The U.S.-based Russian will next play the winner of the quarter-final between France's Kristina Mladenovic and Spaniard Carla Suarez Navarro.
(Reporting by Karolos Grohmann; editing by John Stonestreet)
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