Playing on her 25th birthday, Anisimova fought off three break points early for a 2-1 lead before running away with the opening set in the all-American matchup at Louis Armstrong Stadium.
The players traded breaks to open the second set but Anisimova, the world number 10, never let her grip on the match slip, breaking Krueger's serve in the final game to win the match in one hour and 12 minutes.
"Ashlyn's a great player so I knew it was going to be a tough match," Anisimova said in a post-match on-court interview, shortly before the crowd sang her "Happy Birthday".
Anisimova will face Austrian Lilli Tagger in the second round.