Maria Sharapova, the champion in 2008 and runner-up last year, stormed through 6-0, 6-0 in just 55 minutes and will next play either Croat Petra Martic or Misaki Doi of Japan.
The second seed came into the season's opening Grand Slam without any competitive matches under her belt after a collarbone injury ruled her out of the Brisbane International, but showed no evidence of the problem on court.
She opened her 2013 account on the showpiece Rod Laver Arena on a warm day but without the searing heat that gripped southeast Australia last week, winning her opening serve then breaking her 107th ranked opponent to take a 2-0 lead.
Wearing a summery yellow dress and matching shoelaces, the 25-year-old used her powerful forehand to devastating effect, pushing Puchkova around the court at will as she raced to a 3-0 advantage.
Puchkova, who was playing in her third Australian Open and is yet to go beyond the second round, had little answer to the Sharapova armoury, losing her next service game and netting a forehand to go 5-0 down.
Grunting at full volume, Sharapova then wrapped up the set in just 30 minutes.
Puchkova pushed her to deuce in the first game of the second set but didn't look like breaking her far superior opponent, and she quickly fell behind and never recovered, pushing a backhand long to cap a humiliating defeat.
Playing in her 10th campaign at Melbourne Park, Sharapova is looking to avenge the humbling she was dealt by Victoria Azarenka in the final last year, when she was thrashed 6-3, 6-0 in just 82 minutes.
Sharapova won in Melbourne in 2008 but then suffered a long spell on the sidelines with shoulder problems before climbing back to the top of women's tennis and completing a career Grand Slam at last year's French Open.