Croatia's Martic, who had never beaten a player ranked inside the top 10 heading into this encounter, began the match the brighter of the two players.
She made the most of that advantage by breaking Bartoli twice on her way to winning the opening set 6-2.
Martic claimed another break of serve at the beginning of the second set, only to be be broken straight back by the experienced Bartoli, who was playing in her home Grand Slam.
Having levelled up the set, Bartoli went on to dominate the match as she ensured a deciding rubber would be required to determine a winner.
Both players surrendered their service games in the opening exchanges of the third set.
However, it was Martic who claimed the initiative when she broke Bartoli's serve for a second time. It would prove to be difficult set for 27-year-old Bartoli, who made 14 double faults throughout the whole contest that she ended up losing to her 21-year-old opponent.