France's Bartoli began the encounter at Flushing Meadows sharper than her American opponent, who appeared to be struggling with her service game.
Bartoli took full advantage of Hampton's hesitation to claim a break of serve, before going on to serve out for the opening set.
She appeared to be heading for a relatively comfortable victory when she broke Hampton again early in the second set.
However, Hampton responded by breaking back at the first time of asking, before going on to hold her next service game, which brought the set back level at four games apiece.
Serves were then traded, resulting in the set heading into a tie-break.
The pair were made to wait to contest that breaker though as a heavy rain shower forced play to be suspended for around two hours.
Upon their return to the Grandstand Court, both held their service games up until five points each, before Bartoli's experience shone through to win the breaker and the match 7-5.