A remarkable encounter lasting three hours and 23 minutes was eventually settled in favour of the sixth seed following a topsy-turvy final set.
After the first two sets had been decided by tie-breaks, Sharapova opened up a 5-1 lead in the decider, only to then capitulate by losing five games in a row, spurning three match points in the process.
However, there was another twist to come as Safarova failed to serve out the match and Sharapova, who is seeking a third Stuttgart title in a row, capitalised by wrapping up a 7-6 (7-5) 6-7 (5-7) 7-6 (7-2) victory, her 100th clay-court win.
Sharapova, the world number nine, must reach at least the semi-finals this week in order to remain in the top 10 of the WTA rankings for a 161st week in succession.
Fifth seed Jelena Jankovic came from a set and a break down to scrape past German lucky loser Mona Barthel 2-6 7-6 (10-8) 6-3 in two hours and 25 minutes.
The eighth-ranked Serb broke in the very first service game, but would go on to lose nine of the next 11 as Barthel took control.
However, Jankovic showed plenty of guile - breaking twice in the set to serve for it at 5-4.
The former world number one, though, would cough up six set points in the 10th game, and faced four match points in the tie-break.
From 6-3 down in the tie-break, Jankovic rallied to eventually win the second set on her eighth set point.
Jankovic broke in the sixth game of the deciding set, and despite Barthel's match-point save in the eighth game, Jankovic managed to progress on her fourth match point.
Eighth seed Sara Errani held off a brief fight back to beat Klara Koukalova 6-3 6-4 and register her first main-draw victory in five visits to Stuttgart.
Koukalova raced into a 3-0 lead in set two, but only managed to claim one more game as Errani regained control before breaking to love to seal her progression to the second round.
Carla Suarez Navarro eased past Ekaterina Makarova, winning the first eight games en route to a 6-0 6-4 triumph, and there was a similarly straightforward win for Svetlana Kuznetsova, who defeated Gioia Barbieri 6-2 6-3.
Italy's Roberta Vinci got past German qualifier Annika Beck 6-3 6-2, Russian Anastasia Pavlyuchenkova ousted Austrian qualifier Diana Marcinkevica 6-3 6-2, while another Russian Alisa Kleybanova defeated Croatia's Ajla Tomljanovic 6-2 6-4.