World number two Sharapova looked to be in trouble in the opening set when Ivanovic broke her serve twice to race into a 3-0 lead.
However, the Russian soon found her feet as she broke back twice to take it to a tie-break.
Ivanovic made the breakthrough in the tie-break, but Sharapova fought back with four mini-breaks on her way to a 7-4 win.
The hard-hitting Sharapova broke instantly in the second, only for world number 15 Ivanovic to snatch two breaks of her own and seize the initiative.
The three-time Grand Slam winner eventually came good again as three more breaks saw her close out the match 6-3.