World number 13 and tournament second seed Krejcikova eased to a 6-2 6-0 win over her Czech compatriot Martincova in one hour and five minutes.
The win was the French Open champion Krejcikova's first on hard courts and came courtesy of 26 winners across the 14 games.
At 2-2 in the first set Krejcikova secured a break against the world number 78 and from that point never looked back.
Krejcikova has now chalked up an impressive 20 wins from her last 21 matches.
The 25-year-old's solitary loss in that time was in the fourth round of Wimbledon at the hands of eventual champion, and world number one, Ashleigh Barty.