Sharapova, the 2008 champion and runner-up to Victoria Azarenka last year, executed a 6-0 6-0 demolition of the hapless Puchkova at the Rod Laver Arena to complete a 'Bagel Slam', having also left opponents scoreless at the French Open, Wimbledon and US Open in past years.
The second seeded Russian crushed the 107th-ranked Puchkova in 55 minutes to stay on track for a mouth-watering third round clash with Venus Williams.
"I didn't want to focus on the fact I hadn't played a lot of matches," Sharapova said.
"(I) just wanted to focus on just what was ahead of me and really concentrate and, you know, be aggressive.
"So it was just one of those matches where I didn't try to worry about her too much. I just tried to, you know, think about what I had to do."
After saving two break-points in the opening game, Sharapova needed to do precious little thinking, with her opponent committing 19 unforced errors, including one to bring up three match points.
Sharapova had pulled out of all of her warm-up tournaments after suffering pain in her neck and collarbone, but showed little discomfort as she blasted six aces and 18 winners in bright morning sunshine.
Puchkova surrendered the match with a forehand that floated long.
"When you're out there and playing, you're just focusing on every point and every game and trying to win as many as you can, and today was just a good scoreline," Sharapova said.
"If you win 7-6 in the third, you still won the match."
Already one of the most marketable figures in women's tennis, Sharapova won the French Open last year to complete a career Grand Slam at the age of 25.
American Venus Williams could meet Sharapova in the third round and proved she could be a handful for the second seed by winning 12 successive games to beat Kazakh Galina Voskoboeva 6-1 6-0.
Williams, playing in an eye-catching self-designed dress inspired by watercolours, lost her only Australian Open final to her sister Serena in 2003.
Serena, an odds on favourite to clinch her sixth title this year, gets her campaign underway on Tuesday.
Poland's Agnieszka Radwanska battled through a tricky first set and swept through the second to beat Australian Bojana Bobusic 7-5 6-0 and extend her season-long winning streak to 10 matches.
The fourth seed, who won back-to-back titles to kick off the new year, was never going to match the 6-0 6-0 victory over Dominika Cibulkova in the Sydney International final last week but after a slow start, she gradually overpowered her opponent.
After dropping serve three times in the first set, Radwanska rediscovered her touch on a blustery Margaret Court Arena with wildcard Bobusic's 41 unforced errors helping her advance to a second round meeting with Arantxa Rus or Irina-Camelia Begu.
A Wimbledon finalist last year, Radwanska has made three appearances in the quarter-finals at Melbourne Park and is determined to go deeper this year.
"It's always tough when you have never played someone before," she said. "I will do everything in my power to do better this year."
German fifth seed Angelique Kerber was a 6-2 6-4 winner over Elina Svitolina of Ukraine in just 77 minutes.
Kerber, who reached the semi-finals at Wimbledon in a breakthrough 2012, broke her 127th-ranked opponent five times.
China's Li Na was losing finalist in 2011 a couple of months before she won the French Open and underlined her fine early season form with a 6-1 6-3 victory over another Kazakh, Sesil Karatantcheva.
Li, who won the inaugural Shenzhen Open two weeks ago, will face Belarusian Olga Govortsova in the second round as she continues to thrive under the guidance of Justine Henin's former coach Carlos Rodriguez.
"He's not only a teacher about tennis, not only about technique, he's also helping me get my mind stronger on court," Li said.
Mental fragility has contributed to Sam Stosur's poor previous showings at her home Grand Slam and the ninth seed again failed to convince in a 7-6 6-3 win over Chang Kai-chen of Taiwan.
"I desperately wanted to win out there today, but I didn't necessarily feel it any more than my first rounds in Grand Slams," said the Australian, who was knocked out in the first round last year and at her warm-ups in Brisbane and Sydney.
"I still think there is a load of room for improvement at the moment but it's just the start of the tournament. Hopefully each match I can get a little bit better."