The victory for Williams, who is seeking a seventh Australian Open title and 22nd grand slam trophy overall, could not have been in sharper contrast to that of Sharapova, who preceded her onto Rod Laver Arena.
Sharapova was made to work hard for her 7-5 7-5 victory over 12th seeded Swiss Belinda Bencic before eventually sealing a place in the eagerly anticipated quarter-final in two hours, five minutes.
Williams then swept aside Sharapova's Russian compatriot in 55 minutes with little fuss.
Her only hiccup came in the first game of the match when the 21-year-old raced out to a 0-40 lead and then achieved the second break of the powerful American's serve this tournament to take a surprising 1-0 lead.
Unfortunately for Gasparyan, that was as good as it got against the 34-year-old, who rattled off the next four games on her way to sealing the set in 30 minutes and then breezed through the second in 25 minutes.
The victory was the third successive straight forward win for the American, who has not been pushed in Melbourne since her first round clash with Italy's Camila Giorgi.
She has spent a total of just two hours, 39 minutes on court since beating Giorgi and sounded a coded warning to Sharapova ahead of their clash on Tuesday.
"I just feel like I'm really confident in my game right now, not against her or against any other opponent," Williams said. "I feel if I can just continue to play well, then it could be good."
While her progress through the tournament has been relatively comfortable, Williams said she had another massively motivating factor that could help her up her game on Tuesday. Losing.
Williams has not lost to Sharapova since 2004, a run of 17 successive victories, and holds an 18-2 career record overall against the five-time grand slam winner.
"I think the person who's winning could definitely feel the pressure because there is a lot of expectations," Williams added.
"The person who is losing (could think) 'well, I have lost X amount in a row; I don't have anything to lose'.
"But in this situation, I don't have anything to lose because I'm just here. Every tournament for me is just a bonus at this point in my career."
(Reporting by Greg Stutchbury; Editing by Patrick Johnston)
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