Victor Hanescu also advanced when Dmitry Tursunov retired with a strained left thigh muscle trailing 6-4, 6-6 (3).
France's Gilles Simon will face Japan's Kei Nishikori following a straight forward 7-5 6-3 win over Victor Hanescu.
World number 61 Tomic conceded defeat to Hanescu in Paris after suffering a muscle tear in his right hamstring.
Meanwhile, third seed Murray showed he is finding some form again after a poor season so far with a 6-2 6-1 crushing of Romanian Victor Hanescu.
In Saturday's other matches, eighth seed Gilles Simon of France progressed into the fourth round with a 6-2 7-5 6-2 win against Romanian 31st seed Victor Hanescu.
However, 16th seed Juan Monaco was beaten 7-6 6-4 by Romanian Victor Hanescu, while ninth seed Mikhail Youzhny lost 6-4 4-6 6-3 to former world number one Lleyton Hewitt.
Mathieu is joined in the next round by French compatriots Gilles Simon, the 10th seed, and Gael Monfils after their respective wins over Guillermo Canas of Argentina and Romanian Victor Hanescu.
Andrey Golubev of Kazakhstan beat Germany's Mischa Zverev 6-7 6-4 7-6 and will play Victor Hanescu is the other semi-final after the Romanian eased past home favourite Michail Elgin 6-1 6-4.
Australian Open champion Federer, who had struggled to beat Romanian Victor Hanescu in his opening match after his layoff, said his lack of match practice had counted against him on the crucial points.
In the remaining second-round matches to be completed, Julien Benneteau won 6-0 in the fifth set to edge past Colombia's Alejandro Falla, while Florent Serra needed four tight sets to eliminate Romania's Victor Hanescu.
Swede Robin Soderling is another in the hunt for a place in London and the ninth seed helped his cause with a 6-3 6-4 first-round win over Romanian Victor Hanescu, while Tommy Haas beat Benjamin Becker 7-6 (5) 6-4 in an all-German match.
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