Sharapova lost her first set to Groth, ranked 60th after reaching the fourth round in 2010 French and Wimbledon championships, but fought back to win the next two sets to cruise to the second round. Groth hammered 13 winners in the first set and won by 4-6.
Later in the second and third set Sharapova played well and made Groth to play more shots, inducing 20 unforced errors. Groth donated points with shaky serving, including on the last point of the second set.
Sharapova will face Czech's Iveta Benesova in the second round.
Sharapova had won US Open in 2006, lost at second stage in 2007 and 2009, and missed the tournament in 2008 shortly before having right shoulder surgery.