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Zimmermann was part of a 14-rider breakaway that got away after a fast start to the stage into the Alps, going on to win the stage. The GC battle arrived at a stalemate with race leader Jonas Vingegaard (Jumbo-Visma) unable to gain time on his rivals despite a late attack.
The first mountain stage of the eight-day race saw an intense early battle to try to get in the break before a group of 18 emerged after 43 kilometres on the Côte de Clermont-en-Genevois, only for the peloton to promptly react.
The 18 were caught with 100 kilometres to go but another attack of 14 soon followed with some riders from the earlier group.
They established a three-minute lead with 50 kilometres to race but the final climbs via the Col des Aravis were bound to shake up the race. At 4.5 kilometres from the summit of the 7.8-kilometre mountain pass, Zimmermann emerged with Burgaudeau and Jonathan Castroviejo (Ineos Grenadiers) as the rest of the break faded and the rain began.
The three worked well together to hold off the peloton and the remains of the break, appearing to emerge clear as they approached the final descent to the foot of the Côte de Notre-Dame-de-Bellecombe.
Zimmermann then attacked solo, with Burgaudeau going deep to catch him with 500 metres to go but the Intermarché-Circus-Wanty ride had enough left in the legs to hold on for just the second win of his career and his first at WorldTour level.
"I can't believe it at this moment, I just gave my best and tried everything to be as good as possible, it worked out perfectly," the German rider said.
"Yesterday I felt strong but it didn't work out and today I tried again and like I gave it everything.
"I knew the parcours really well because in 2018 there was a finish up here in the Tour de L'Avenir and I was in a similar situation but the favourites sprinted around me with 200 metres to go.
"Today it was the other way round, I could attack on the climb and go full gas and in the end take the sprint, I'm completely speechless."
Meanwhile, Vingegaard attacked in the final kilometre of the 170.2 kilometre stage to test his rivals but was kept in check and finished safely in the GC group to keep the leader's yellow jersey.
The Dane remains clear of Aussie Ben O'Connor (AG2R-Citroën) by one minute and 10 seconds, with Julian Alaphilippe (Soudal-QuickStep) third at one minute and 23 seconds ahead of this weekend's showdown in the high mountains.
"I think they'll be super hard stages, they're long mountain stages, so hopefully I'll feel good," Vingeaard said.
"I'm looking at the whole top ten, you can't give space to anyone. You have to look at everyone and not let any gaps go."
Stage 7 of the Critérium du Dauphiné will see the peloton take on a 147.9-kilometre route with climbs on the Col de la Madeleine, the Col du Mollard and then up further to the 2066 metre-high Col de la Croix de Fer. Watch all the action from 10:55pm AEST on SBS On Demand and 11:15pm AEST on SBS VICELAND.
