Bartoli enjoyed a blistering start on Tuesday evening as she raced to a 4-0 lead over the Russian.
Rain then halted proceedings before the players were allowed back on court on Wednesday afternoon.
Sharapova broke back when play resumed but she was unable to get closer to Bartoli who won the set 6-3, her first in four meetings against the world number three.
Tensions were running high between the players out on the Arthur Ashe Stadium as they both failed to hold serve at the start of the second.
Sharapova finally made the breakthrough in the seventh game as an unstoppable forehand gave her the break and a 5-3 lead before she served out the set 6-3.
After an aggressive start to the third, the 2006 winner broke to take a 2-1 lead thanks to another powerful forehand winner.
However, Bartoli broke back instantly to level the set at 2-2.
Sharapova then saved two break points to hold for 3-3 before a final break allowed her to serve out the contest 6-4.
She will now meet world number one Victoria Azarenka for a place in Saturday's final.