The Russian held serve to reach 6-5 after hitting an overhead winner.
Bacsinszky held serve after striking two crosscourt backhand winners to enter a tiebreaker.
Sharapova netted two crosscourt backhands to trail 0-2 in the tiebreaker before hitting a down the line backhand lob wide to fall behind 0-3.
The Swiss sent a backhand down the line wide before hitting a backhand down the line winner to lead 4-1.
Bacsinszky double-faulted before striking a powerful crosscourt backhand which forced a Sharapova left-handed forehand error for a 5-2 lead.
The Russian struck an inside out crosscourt forehand wide to trail 2-6 and face setpoint.
Sharapova saved setpoint by staying in an extended point before striking a forehand down the line winner to reach 3-6.
However on set point number two, it was the Swiss’ turn as she struck a forehand down the line winner to take the set 7-6(7-3) after one hour and eight minutes of play.
In set two, Sharapova steadied her game to take a 2-0 lead before the Swiss hit back to level the set at 3 games all.
Bacsinszky struggled serving at 3 all with her service game going to three deuces over the course of eight minutes before Sharapova hit an inside out crosscourt forehand volley winner to reach the final breakpoint of the game.
The Swiss double-faulted to lose serve and fall behind 3-4.
In her following service game, Sharapova netted two crosscourt backhands then committed two forehand errors to drop serve to reach 4 all.
Both players then held serve to level the set at 5 games all.
With the Swiss serving, Sharapova hit a forehand down the line wide to trail 0-15 before Bacsinszky struck a crosscourt backhand winner to lead 30-0.
The Russian struck a crosscourt forehand volley long to fall behind 0-40 before hitting a forehand return long as the Swiss held serve to lead 6-5.
Serving to stay in the match, Sharapova struck a crosscourt backhand long then netted a crosscourt forehand to trail 0-30.
Two powerful forehand winners from the Russian: one crosscourt, the other down the line, leveled the score at 30 all.
However Sharapova wasn’t able to hold on to her inspired play as she struck a forehand down the line long to face matchpoint.
A netted crosscourt backhand from the Russian ended the match after 2 hours and 16 minutes of play.
For the match, Sharapova would finish with 37 winners to 43 unforced errors including seven double-faults.
"She had a really good serving day," Sharapova said of Bacsinszky. "I don't
think I did much on my returns, something that's a strength of mine, and I just
didn't feel like I used that to my advantage."