Martin, whose climbing punch on the steepest hills, made him one of the pre-stage favourites, held off a last ditch pursuit from the French rider Pierre Latour, a teammate of Romain Bardet, who was third overall in the 2017 Tour.
Ireland's Daniel Martin celebrates as he crosses the finish line to win the sixth stage of the Tour de France.
Dumoulin suffered a puncture inside the last 6km and then copped a 20-second time penalty for taking a tow back to the front.
The likes of Vincenzo Nibali, Richie Porte, Geraint Thomas, Nairo Quintana, Mikel Landa and even Peter Sagan were part of the group - although defending champion Chris Froome (Team Sky) found himself on the other side of a slight split to concede five seconds to many of his GC rivals, while Colombian Rigoberto Uran (EF Education First-Drapac) was a further three seconds in arrears.
"I felt comfortable", he said.
Dumoulin, the time trial world champion and 2017 Giro d'Italia victor, was slowed by a tire puncture at the foot of the final ascent and lost 53 seconds.
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Dumoulin and his Sunweb team compounded the mechanical mishap by getting a 20-second penalty when Dumoulin stayed too close to the team vehicle while trying to catch the pack, thereby benefiting from its draft that pulled him along.
"It was an early break but it was my only opportunity for the stage win as I'd never have got it in a sprint", explained Martin.
Greg Van Avermaet retains the yellow jersey and remains first in the general classification for the fourth consecutive stage.
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).
Martin was one of several team leaders along with former Tour victor Vincenzo Nibali and two-time runner-up Nairo Quintana who were caught off-guard by an attack by Quick-Step 100 kilometers into the stage during a straightaway that was exposed to crosswinds.
Friday's flat 231-kilometre leg from Fougeres to Chartes is the longest stage of this Tour.
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