Seeded for the first time at a major, Gajdosova appeared to enjoy her new status as she overpowered the world number 96 in one hour and eight minutes on centre court at Roland Garros.
She will play the winner of Italy's Corinna Dentoni and qualifier Anabel Medina Garrigues of Spain in the next round.
The 24th seed joins compatriots Samantha Stosur and Anastasia Rodionova as Australia's remaining players in the women's draw.
It had been an emotional past few weeks for both players.
Gajdosova officially split from her husband last month, while Razzano's fiance died a fortnight ago following a nine-year battle with a brain tumour.
After bringing up the win, the Australian appeared to express her condolences to Razzano at the net.
Although she had the odd wobble on serve in the first set, Gajdosova saved six of seven break points and always looked like she was a chance of breaking Razzano.
The Frenchwoman did her best to stay in the contest but could not handle the power of Gajdosova's ground strokes in cool conditions in Paris.
Gajdosova enjoyed a breakthrough season in 2010, using fourth round appearances at Roland Garros and Wimbledon to propel herself up the rankings.
And on Tuesday's showing, she looked well on track for a possible third round meeting with 15th seed Andrea Petkovic of Germany and potential fourth round showdown with Kim Clijsters.
- AAPTags: sport, tennis, france First posted May 24, 2011 21:00:00