Sharapova dominated her opponent in every department as she raced through the first set in just 23 minutes.
Shvedova, a qualifier from Kazakhstan, offered more resistance in the second but was no match for the world number two.
Sharapova had not played a competitive match since the WTA Finals in October. But there were no signs of rust as she cruised into the quarter-finals.
"It certainly felt good to start (well) after not playing a match for a couple of months," Sharapova said.
"I wanted to start off sharp and try to do the right things."
Sharapova broke her opponent five times throughout the match, but had to save two break points on her own serve in the second set.
She said this was important in stopping any chance of a Shvedova comeback.
"She lost the first set in her previous match (against Sabine Lisicki) 6-0 and ended up winning the match in a tough three-set battle, so you never know," Sharapova said.
Sharapova will now play the winner of the clash between seventh seed Carla Suarez Navarro of Spain and Croatia's Mirjana Lucic-Baroni.
Earlier, third-seeded German Angelique Kerber remained on course for a semi-final showdown against Sharapova when she crushed Russian qualifier Daria Gavrilova in straight sets.
Kerber needed just 90 minutes to see off Brisbane-based Gavrilova 6-3, 7-5.
"I think it's good to be now in the quarters and have a lot of matches before Melbourne," Kerber said.
She will now take on Ukraine's Elina Svitolina, a 6-3, 6-2 winner over Croatian Ajla Tomljanovic.
Defending men's champion Lleyton Hewitt suffered a shock loss at the hands of big-serving fellow Australian Sam Groth.
Groth blasted 14 aces and won 89 percent of his first serves to overpower Hewitt 6-3, 6-2 in just 58 minutes.
Fifth seed Kevin Anderson was another casualty in the men's draw, with the South African falling to Polish qualifier Lukasz Kubot 7-6 (7/3), 6-4.
Seventh seed Alexandr Dolgopolov, a finalist in Brisbane in 2012, cruised into the second round with a 6-2, 6-3 win over Argentina's Carlos Berlocq.
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