In her debut WTA Tour main-draw event, the Tier-II tournament in Los Angeles 2003, Kutuzova beat top-50 player Lina Krasnoroutskaya in the first round, and top-30 player Alexandra Stevenson in her next match, before losing in the third round to the then-world No.

In 2009, she reached the final of the $100k event in Torhout, losing to Karolina Šprem, in straight sets.

Kutuzova suffered shoulder problems throughout her young career which stalled her progression on the main tour.

After having over a year off-tour, Kutuzova used her protected ranking to enter her first big event, the 2011 Sparta Prague Open, where she lost to Katarzyna Piter in round one.

She also entered Roland Garros using her protected ranking, but was beaten by Chanelle Scheepers, also in the first round.