Playing a record 80th main draw match at Melbourne Park against an 18-year-old on her first trip Down Under, Williams was merciless under the lights of Rod Laver Arena, blasting 24 winners and winning all 10 points coming into the net.
"I love your game and that forehand, it is really awesome,” said Serena after the match.
Kasatkina raised rambunctious cheers from sympathetic fans in the terraces when she prised a game in each set but Williams finished full of running, closing out the match in 44 minutes when her frazzled opponent pushed a forehand wide.
And while the scoreline was one-sided, Williams paid a nice tribute to her opponent at the net, telling her how much she liked her game, and then saying in her post-match interview what a "bright future" the young Russian has.
Williams, bidding for seventh title at Melbourne Park and a 22nd grand slam trophy, faces another unseeded Russian in Margarita Gasparyan in the next round.