The former top-ranked player needed just five points to advance in the Wimbledon warm-up tournament after her match had been delayed overnight by bad weather.
Victory over the 19-year-old US Fed Cup player continued Sharapova's grass court build-up to what she hopes will be another assault on the Wimbledon title in 12 days' time, though it meant that she was obliged to play twice in a day.
Florida-based Sharapova had twice been match point up against the promising American on Wednesday, but with the rain beginning to turn from drizzle into a downpour they had had to come off with Glatch holding a point to reach 5-5.
Sharapova's first shot on resumption was a brilliant forehand return of serve, followed by a winning approach shot, which brought the score back to deuce.
She reached match point with a quieter return of serve which Glatch struck beyond the baseline, only for the teenager to save the third match point with a fine winning serve. When Sharapova earned a fourth match point, however, with a short low return combined with a winning pass, she converted it.
Sharapova forced Glatch to come in again with a short return, and this time Glatch over-hit.
Was this the shortest amount of time she had spent on court? "Probably, yes,'' she giggled.
"It's never easy, but everyone has to deal with these situations,'' she added. "It's tricky but I'm glad I could make it.''
Asked if the shoulder, which kept her out of the game for almost 10 months, was now fine, she replied: "I hope so. We will see. I play the best I can and just get the job done.''
The next job was a last-16 meeting with the seventh seeded Francesca Schiavone, the former top 20 Italian, who overwhelmed Ukraine's Mariya Koryttseva 6-1, 6-1.
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