Valtteri Bottas headed the time charts in both sessions at the Sochi Autodrom on Friday, but it was Hamilton's turn to lay down an ominous marker ahead of qualifying.
Hamilton has won four of the six times the race has been staged on the site of the venue for the 2014 Winter Olympic Games.
And the 35-year-old Englishman will be boosted by his display here as he goes in search of win number five on Russian soil, and more importantly, Schumacher's all-time tally.
British driver Lando Norris finished last in his McLaren, 2.7 seconds behind Hamilton.
Qualifying for the 10th round of the campaign gets under way at 3pm local time.