Gauff made a commanding start against Alexandrova but came under pressure as she served for the first set.
She had to withstand five break points in a sixth game lasting almost 10 minutes before she eventually converted her third set point.
Gauff was the first to face break points in a competitive second set but struck first against an improving opponent to lead 4-3.
Alexandrova, competing in the fourth round in Paris for the first time, offered resistance with an immediate response – but Gauff finished the stronger and sealed victory with a run of three straight games.
Gauff, described recently by compatriot Frances Tiafoe as ‘Little Miss Mature’, said: “Most people do say I’m mature. I feel like playing tennis forces you to grow up faster.
“When I was in school, I would always be the first one to class. I remember getting on the yellow for the behaviour chart once, and that was like the worst day of my life.
“I’m definitely someone that prides myself on being a good example.”