But on the all-time Tour de France stage win list, the Briton's latest triumph now places the 31-year-old equal second with France's Bernard Hinault.
Kittel, 28, ended the day with a time of 5.28.30 hour and an average speed of 43.2 kilometres per hour (27 miles per hour).
Slovak Sagan (Tinkoff) came in third, while Cavendish, chasing a 29Tour stage win, got boxed in and could only finish eighth, surrendering the lead to Sagan in the points classification.
A metre from the line, Greipel looked sure to win, yet somehow Cavendish stretched out his bike to snatch victory.
Cavendish, who was well positioned by his teammates, managed to live up to the expectations and won the stage.
The finish here is a little reminiscent of Stage 4 in the 2015 Tour de Suisse, where Michael Matthews was able to overcome Peter Sagan in the closing stages. Find us on Facebook too!
He had won far more comfortably on Saturday s opening stage in Normandy, after which he took young daughter Delilah up to the victory podium with him.
Mark Cavendish, wearing the green jersey, crosses the finish line ahead Germany's Andre Greipel, left, and Peter Sagan of Slovakia, wearing the overall leader's yellow jersey, to win the third stage of the Tour de France. It feels like my first stage win again. I felt super proud and so happy.
This was how unbelievably close the Tour de France finish was today
In his debut in the race, Fortuneo-Vital Concept's British sprinter, Dan McLay, got his third top-ten finish in four days and his highest placing yet as he took seventh place.
Kittel, who wore the race leader's yellow jersey in 2013 and 2014, joined the Etixx Quick Step team from Giant-Alpecin for this season, replacing the departing Mark Cavendish.
Oliver Naesen of IAM Cycling and Trek-Segafredo's Markel Irizar, the final members of the day's break, were swept up with just 7km remaining of the stage from Saumur, at 237.5km the longest of this year's race.
Wednesday's stage includes a lumpy finish that will probably shred the peloton, but on Tuesday there will nearly certainly be a bunch sprint.
Kittel had to wait for confirmation of his win having only edged out Frenchman Bryan Coquard by millimetres.
"Today was a very relaxing day for us because in the breakaway there was only one rider", said Sagan.
In reality, however, with the rule applying only in the event of a mishap, the general classification riders continue to go hell for leather because if there is a split of one second or more then you will be awarded the same time as the group you come in with.