They built a lead of nine minutes before the domestiques of the sprinters set about ruining their ambitions. The sprinters first overcame Elmiger, then a defiant Bauer 30 metres from the line.
Bauer, born in Takaka, based in Girona, crossed the line distraught, 10th in the midst of the sprinters.
Paul Jesson in 1980 and Greg Henderson, 2009, won stages of the Vuelta Espana and are the only New Zealanders to win a stage of one of the three grand tours.
Henderson withdrew from this year's Tour de France after a crash.
Jesson watched Bauer's performance from his Christchurch home. "Oh, yes, I felt for him," Jesson told the Herald.
Jesson won from a long-range breakaway, holding off the favourites to win alone by 15 seconds - enough time, he said, to zip up his top, raise his hands aloft and enjoy the moment. He survived from a break of 17 riders that dwindled as they climbed two category 1 mountains.
"He's a very strong rider and it was so close," he said of Bauer. "He'll get another chance, hopefully."
Just one month after his Vuelta stage win, Jesson's professional career was ended by a crash in the Duaphine Libere in Evian Les Bain which resulted in a leg being amputated. He resumed racing with a prosthetic and became a world champion in 1998 at the IPC Paracycling World Championships.
"It's a childhood fantasy to win a stage of the Tour for any cyclist, and especially for a Kiwi because not many of us ever get the chance," Bauer said today. "I really gave it absolutely everything."
"It would have been a career defining moment. I could retire tomorrow. I would be a happy man," he told ONE News. "So I guess I saw that all coming true in the last kilometre and then I realised it wasn't coming true in the last 50 metres ..."
Bauer and Elmiger led the stage from the starter's gun as the race rolled away from the Alpine town of Tallard, through Provence and the Midi, battling through a storm and entering the suburbs of the Roman city with almost a minute advantage on the main field.
"We really came together as a team and decided this morning that one of us would be in the move no matter what it took. I hadn't planned on it being a two-man move. Me and Martin managed it pretty well between ourselves. I think we both had decent legs in the finale, I felt I had the upper hand in the last 20km. I just waited to pounce. Maybe I waited a little too late."
Julian Dean and Chris Jenner have won Tour de France teams time trial stages.
Arrgggghhhhhhhhhhhhhhh!!!!!! Jack!!!!! Poor Jack. Oh Jack. Im Bleeding for you. Amazing ride.