Five-times Grand Slam champion Sharapova, who won at Flushing Meadows in 2006, struggled with her serve at times in the opening set but Schnyder failed to take full advantage.
The Swiss retired from tennis after being beaten in the first round of the French Open in 2011 but returned in 2015 and last week became the oldest woman qualifier to reach the main draw of a Grand Slam at the age of 39 years and eight months.
She was handed an early break by Sharapova after the Russian made three double faults in her opening service game, but double faulted on break point on her own serve to hand the initiative straight back.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
With the first four service games all broken, Sharapova held for the first time to take a 3-2 lead and, having got her nose in front, found both her rhythm and serve and began dictating play from the baseline.
The 22nd seed wrapped up the first set in 40 minutes and was leading 5-1 in the second before Schnyder embarked on a remarkable rally.
The Swiss started to take the pace off the ball to gain a greater degree of control and the approach paid dividends as Sharapova's error count mounted.
The Russian, who hit 22 winners but made 46 unforced errors, needed four match points to end Schnyder's resistance as the match went to a tiebreak, eventually sealing victory with a powerful forehand winner.
(Reporting by Simon Jennings; Editing by Peter Rutherford)
