Ivanovic, who has slumped to 58th in the rankings since winning the French Open in 2008, was seeking to reach her first WTA Tour final since March 2009.
Ivanovic, who occupied top spot after winning the French Open in 2008 but is now ranked 16th, recorded a 6-3 6-2 against the Danish fourth seed -- who lost her No. 1 ranking following Victoria Azarenka's triumph at January's Australian Open.
Ivanovic, French Open champion in 2008, was pleased with her form and told reporters she still harbors hopes of reaching No. 1 in the world.
Serbia's 2008 French Open champion will next play Dutch world No. 91 Michaella Krajicek.
Over the last five years, counting the 2008 French Open, Federer has played 108 completed Grand Slam matches against non-Big Four players.
None have the talent of Sharapova and have won a single Grand Slam tournament combined in their careers (Ivanovic, 2008 French Open).
Another golfer, Australia's Adam Scott, has recently rekindled his romance with glamorous Serbian tennis star Ana Ivanovic, the 2008 French Open champion.
Since Ana Ivanovic took the top spot by winning the 2008 French Open, no No. 1 has played up to the part.
The Belgian, 27, retired on the eve of the 2008 French Open, a tournament she had won four times along with two US crowns and one Australian Open.
Ivanovic has suffered a slump in form since winning the 2008 French Open, but has shown encouraging signs this year rising seven places in the rankings to 15th.
CNN: Fed Cup: Serbia makes history in first semifinal showdown
Meanwhile, former world number one Ana Ivanovic continued her disappointing grand slam form since winning the 2008 French Open as she was bundled out by 36th-ranked Gisela Dulko 6-7 7-5 6-4.
But the 2008 French Open champion, who also beat Azarenka on her way to the semi-finals in Rome in May, fought back to set up a second-round clash with Yaroslava Shvedova.
BBC: Ana Ivanovic beats Victoria Azarenka at Cincinnati Open
The women's matchups Sunday to decide quarterfinal berths are: 15-time major champion Serena Williams against No. 15 Roberta Vinci, 2008 French Open titlist Ana Ivanovic against No. 4 Agnieszka Radwanska, 2009 champion Svetlana Kuznetsova against No. 8 Angelique Kerber, and 2012 runner-up Sara Errani against No. 20 Carla Suarez Navarro.
Djokovic reached a career high ranking of number two in the world earlier this year, Jankovic went one better and briefly topped the women's rankings in 2008 while Ivanovic claimed grand slam glory at the French Open in the same year.
It was her second success at Charleston, following a 2008 triumph, and fourth on clay after winning both the French Open and the Italian Open in 2002.
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