Wales led 10-3 at the break thanks to winger Cuthbert’s superb individual try but France remained firmly in the game with two Welsh penalties hitting the woodwork.
And Philippe Saint-Andre’s side emerged in the second half determined to rain on Wales’ parade.
A penalty from Dimitri Yachvili, his second of the match, and Lionel Beauxis ensured they stayed in touch but a pair of kicks from Leigh Halfpenny combined with some tremendous defence ensured Wales won their third Grand Slam in eight years.
The game was preceded by an emotional minute’s silence in tribute to former Wales Grand Slam winning captain Mervyn Davies, who died on Thursday, as well as Jock Hobbs, the ex-All Blacks skipper.
But a combination of nerves and the slippery conditions with the open roof at the Millennium Stadium meant both sides struggled to settle into a meaningful rhythm.
It was the visitors who drew first blood on ten minutes when Gethin Jenkins was penalised for interrupting a French maul and Yachvili slotted the three points.
Wales were struggling to make inroads into a teak-tough French defence but when they failed to roll away from a penalty on 15 minutes, Rhys Priestland stepped up to the tee only to send his kick against the upright.
But eventually the pressure told on France. Captain Thierry Dusautoir was clattered by Dan Lydiate and in a flash Alun Wyn Jones was able to turn the ball over and Cuthbert picked a tremendous angle to sorch past William Servat and leave full-back Clement Poitrenaud flat footed for the game’s opening try.
Halfpenny converted and added a penalty on 32 minutes after some superb work from Jonathan Davies in scragging Alexis Palisson.
The remainder of the half was dominated by the hosts and Jamie Roberts belied his reputation as a battering ram with a delicate chip and gather but Wales could not pierce a stretched French defence.
In their desperation, Yachvili conceded a penalty but Halfpenny’s kick hit the posts to leave the score at 10-3 to the hosts.
Warren Gatland was forced into a reshuffle at halftime when captain Sam Warburton could not continue with a shoulder injury so Ryan Jones entered the fray.
But it was another replacement, debutant Jean-Marcellin Buttin, who had made the first decisive intervention of the second half when he attacked down the left and chipped ahead and forcing Jenkins to stray offside.
Beauxis’ penalty made it a four-point game although the French fly-half was off target with a drop goal shortly afterwards as the visitors showed far more attacking intent than they did in the first half.
And it was while Wales were defending that they forced a penalty out for not releasing and Halfpenny landed a monster kick from just inside his own half.
But life continued to be uncomfortable for the majority inside the Millennium Stadium as Lydiate only just hauled down the lively Buttin who had caught Wales napping from Beauxis’ crossfield kick.
Some more desperate defence – led by the tireless Lydiate – again kept France out after an up-and-under caused panic in the Welsh 22.
The concession of a penalty at a scrum allowed Yachvili to make it 13-9 but almost immediately replacement Francois Trinh-Duc gave away a penalty after throwing the ball away after being forced into touch.
Halfpenny held his nerve to restore the seven-point cushion with four minutes remaining and they showed some great game management to prevent France threatening again.
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