Australian Michael Matthews (Sunweb) won the bunch sprint for second eight seconds later ahead of Yves Lampaert (Quick-Step Floors) at the end of the 189km stage from Gansingen to Gstaad.
"I'm super happy, we didn't expect to stay away on a day like today but when we had two minutes at the bottom of the climb, then suddenly the break started to believe it was actually possible. I am over the moon," Juul Jensen said.
"Coming out of a great Giro with Mitchelton-SCOTT, I felt I had good form and when he (Peters) attacked I kept him at a relatively close distance and I could see that he was maybe taking the corners slightly slower then I was. I was closing the gap and decided to make the most of it before it was too late.
"It was a long three kilometres on the airfield here but it is a fantastic feeling. Especially here, being in Switzerland with the king of Switzerland on the team, I am happy to pull out a good result."
Juul Jensen was aggressive in making the six-rider break which worked to a six-minute lead on the peloton. The stage continued that way even as the rain came down and time gap tightened.
With 10km to go and the peloton bearing down on the pair, Juul Jensen and Nans Peters (AG2R) sensed the timing was right for someone in the break to take the win.
Peters looked to have the legs when he created a small gap but Juul Jensen bridged back and then attacked with three kilometres to go and had enough left in the tank to hold his effort to the finish.
The general classification remained unchanged with the BMC trio of Stefan Kung, Greg van Avermaet and Australian Richie Porte leading.
On the 155km Stage 5 menu from Gstaad are three steep climbs culminating in a summit finish at Leukerbad which should reshape the race for the overall.