Less than 30 seconds after the restart Benzema tapped in Ribery's fine cross from the edge of the six-yard box to put the result beyond any doubt, with Jeremy Menez adding a fourth goal in added time.
France was occasionally troubled by the pace of Estonia's counterattacks but looked in buoyant attacking form ahead of their Euro 2012 kickoff against England on Monday.
After just 25 seconds, Diarra was holding his knee in pain having kicked the ground when playing a pass but the Marseille midfielder, to Blanc's relief, was quickly back on his feet and able to continue.
Estonia took advantage of a subdued start to the match to create two early chances in quick succession. First, Tarmo Kink found himself played through on goal down the left-hand side but shot wildly across goal. Philippe Mexes should have dealt with the subsequent cross from the opposite flank but mishit his clearance straight to Ojamaa, who just missed the far post with a low shot.
Mexes was again in trouble when Oper counterattacked down the left wing but the AC Milan defender did just enough to prevent Ojamaa from converting his strike partner's cross.
Eventually, France's offensive quality shone through. Ribery volleyed a perfect finish past Estonia goalkeeper Sergei Pareiko after a wonderful flick from Benzema had set the Bayern Munich winger through on goal.
From there, French confidence flowed. Ribery had delighted the crowd with one nonchalant touch to Patrice Evra before Cabaye came agonizingly close to making it 2-0 with a swerving effort from 25 yards that shaved the post.
After his low cross had almost been diverted into the Estonia goal by Taavi Rahn, Benzema brilliantly doubled France's lead. The 24-year-old, lurking at the back of the penalty area, controlled a high ball after a corner was only partially cleared and curled a sumptuous shot beyond Pareiko.
It took Benzema just 27 seconds to pick up where he left off after the break. Ribery raced away down the right wing and aimed an inch-perfect cross beyond the stranded defender Rahn for the striker to convert from close range.
Estonia's surges into French territory had become less frequent since Ribery had broken the deadlock but the Blueshirts did engineer enough space for Sander Puri to shoot just wide after a swift move upfield on the hour mark.
For the most part, though, it was all too easy for France. The crowd was more interested in their Mexican wave when Benzema danced across the Estonia defence before testing Pareiko with a driven shot.
A fourth finally arrived when substitute Menez slammed home a left-footed shot from close range following Olivier Giroud smartly diverted a low cross by Evra.
Blanc rung the changes throughout the second half to ensure further injuries to his squad were avoided, with Laurent Koscielny deployed out of position as a holding midfielder in the absence of M'Vila and Matuidi.
Some work on Rami and Mexes' partnership may be required over the weekend but otherwise Les Bleus will take heart from a convincing final showing ahead of their big kick-off in Ukraine.
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