I had really good legs and when I went my legs kept coming and coming, " Martin said.
Martin counterattacked when Richie Porte jumped ahead and nobody immediately tried to reel him in.
The peleteon split in three just under the 100 kilometre mark with Quick-Step and the main contenders in the first chasing group, followed by a second group which included Movistar's Nairo Quintana and Mikel Landa, Vincenzo Nibali (Bahrain Merida), Dan Martin (UAE), Ilnur Zakarin (Katusha) and Astana's Jakob Fuglsang. Pierre Latour 3. Alejandro Valverde 4.
Britain's Adam Yates finished sixth on the day in the pack three seconds back, and has vaulted above Froome in the overall standings. When we got closer to the finish I was a bit nervous because of the head wind and I didn't think it was going to happen.
Martin began the day one minute and 40 seconds down on Greg van Avermaet in the yellow jersey, but picked up 13 seconds to move up to 21st overall in the general classification.
Tom Dumoulin, victor of the 2017 Giro D'Italia, suffered badly following a mechanical issue with only 5km to go, dropping 40 seconds on the leaders.
Bardet was already trailing Froome, and after losing 28 seconds is now 1:45 off the leader's pace after he broke his back wheel and had to change bikes with Tony Gallopin. "There are a lot of twists on the Tour and this time luck was not on our side".
Van Avermaet, a BMC support rider for Porte, kept the yellow jersey for a third straight day.
Joining Porte in those time gains was Irish stage victor Daniel Martin (UAE), Spaniards Alejandro Valverde (Movistar) and Mikel Landa (Movistar), Briton Adam Yates (Mitchelton-Scott), Welshman Geraint Thomas (Sky), Colombian Nairo Quintana (Movistar), Italian Vincenzo Nibali (Bahrain-Merida), and Dane Jacob Fuglsang (Astana).
It was in 2011 when the Tour first finished a stage on the steep, two-kilometre climb to Mur-de-Bretagne. Bardet, who suffered a broken wheel, was forced to swap bikes with a teammate and lost over half a minute to the stage victor Martin.
Martin becomes just the third Irish rider to win two or more stages on the Tour alongside Ireland's cycling royalty Sean Kelly and Stephen Roche.
Friday's flat 231-kilometre leg from Fougeres to Chartes is the longest stage of this Tour.