It is a fifth stage win for UAE during this year’s race, with reigning champion Pogacar claiming the other four.
“It is a very special victory,” said Wellens. “Everybody knows the Tour de France but not many people win in the Tour de France, so it was very beautiful.”
After three gruelling days in the Pyrenees mountains, the 166 remaining riders faced a transitional stage before the second and final rest day of this year’s Tour in Montpellier.
The stage looked set for a breakaway win and Wellens sensed his opportunity on the last of the three categorised climbs, up the Pas du Sant 55km from the line.
Wellens emerged from a lead group of eight on the ascent, along with Michael Storer, Quinn Simmons and Victor Campeanaerts.
The group briefly reformed on the long descent to Carcassone but moments later, Wellens attacked with 44 km to go and the chasers never looked like closing the gap.
“I felt super good today,” Wellens added. “On the last climb of the day I felt really good. I knew the others felt really good but I knew I had to go solo. At the top of the climb I found my moment and I felt I had the legs to keep it to the end.
“I knew I had to enjoy the moment and kept riding until the end so I had a big gap to enjoy it and maybe put my bike in the air after the finish – but I was so happy I forgot to do it.”
Three-time Tour winner Pogacar added: “I am more happy for him today than when I win. Beyond happiness.”
The race resumes on Tuesday with a 171.5km ride from Montpellier and ending with a mammoth climb up Mont Ventoux.
Pogacar said: “This week was one of the hardest second weeks of the Tour that I have ridden because of the terrain, the time trial on the climb [on Friday] and yesterday with 5,000m of elevation [gain].
“The gap is now big but we still have big mountains to come. We need to fight until the end.”