The third seed and 2009 champion will face either close friend and Swiss compatriot Stanislas Wawrinka or seventh-seeded Frenchman Jo-Wilfried Tsonga for a place in the quarter-finals.
Federer, the 2009 champion and playing in his 46th consecutive grand slam, had been pushed by Tipsarevic in a five-set marathon in the third round of the Australian Open in 2008.
But there was to be no such drama on Friday.
Federer romped through the first set in just 19 minutes with two breaks of serve, allowing his 26-year-old opponent just 10 points.
On a chilly Suzanne Lenglen court, where the temperature hovered around 19 degrees, the Swiss was a break to the good for a 3-2 lead in the second set and backed it up for 4-2, fighting off the only break point he faced.
Tipsarevic, the 29th seed, who had never got beyond the third round in his seven previous visits to Paris, was soon two sets down when he dumped a backhand service return into the net.
Federer laid a further foundation for victory with a break in the first game of the third set and the match was over in just an hour and a half when the sunglasses-wearing Serb popped a lazy backhand out of play.
- AFPTags: sport, tennis, france