Safin ousts Mathieu to put Russia into Davis Cup semis
Sebastien Grosjean had handed France a lifeline earlier, beating Igor Andreev to level proceedings at 2-2.
But Mathieu proved to be no match for Safin with his country exiting the competition at the quarterfinal stage for the third year in a row at the hands of the Russians.
The Frenchman, who had beaten Nikolay Davydenko in his singles rubber on Friday, struggled to keep pace with Safin, a late inclusion for the decider at the expense of Mikhail Youzhny.
The big-serving Russian, who lost two of his three previous meetings with Mathieu, produced 15 aces to win 7-6 (7/3), 6-3, 6-2 in two hours 28 minutes and advance his side to a showdown with Germany who beat Belgium 3-2 in Ostend.
"I didn't expect our skipper would put me on court this weekend and of course I never expected it would be so easy as I could not find my form in two recent months," said Safin.
Hours earlier Grosjean had beaten Andreev 7-5, 4-6, 2-6, 6-3, 6-4 to pull France level.
Grosjean, whose poor service game was a big factor in the doubles defeat, alongside Michael Llodra, to Russia on Saturday, sealed victory on a second match point after nearly four hours of playing his first match against Andreev.
"I tried to play as aggressively as possible, and today I managed it," said Grosjean. "That was the only way to win as Andreev plays really powerful tennis."
Grosjean, whose season has been relatively disastrous, could feel relieved.
France captain Guy Forget had made a late switch, deciding to field Grosjean instead of French number one Richard Gasquet, who had lost to Youzhny on Friday.
Forget's faith in the out of form Grosjean paid off as he produced the best match of what has been a poor season so far to pull the visitors right back.
With little to lose, Grosjean decided to go out and take all the risks, especially on his returns of serve.
It seemed to give him the psychological advantage, and he surged to win the first set inside the hour.
Andreev moved up a gear in the second, adding power and precision to his game and he broke early for a 3-1 advantage which he kept to win the set and pull level.
Grosjean was easily overcome in the third set, with Youzhny breaking the 28-year-old's serve twice to give Russia a sniff of claiming a place in the last four.
However Grosjean dug deep. In the next two sets he rained down a series of confidence-boosting winners which left Andreev struggling to keep his nerve.
Grosjean went on to break the Russian's serve in the eighth game of the fourth set to pull level at two sets all.
Andreev fought hard and the 23-year-old managed to survive one match point before Grosjean's determination paid off.
On Friday Mathieu had given France the advantage after he battled back from a set down to beat Davydenko 2-6, 6-2, 6-1, 7-5 in the opening rubber.
Youzhny than beat Gasquet in a marathon five-setter 6-2, 6-3, 6-7 (8/10), 5-7, 8-6 to level proceedings at 1-1.
On Saturday Davydenko and Andreev put Russia 2-1 up with a doubles victory over Llodra and Grosjean 3-6, 7-5, 6-3, 3-6, 6-3.
France had now been bundled out of the tournament's quarterfinals three years consecutively by Russia, who also beat France in the final in 2002.