Pedersen, a Dane who had finished second and third in sprints earlier in the Giro, was fastest after the peloton caught a two-man breakaway in the last 300m. He also completed the set of individual stage wins in the major tours.
After a 162km stage, that started and ended in Naples and took in Mount Vesuvius and the Amalfi coast, two 36-year-old veterans, Australian Simon Clarke and Italian Alessandro De Marchi seemed to have the stage in their grasp as they led by 16 seconds entering the last kilometre.
But the former teammates stopped cooperating a little too soon.
Fernando Gaviria of Team UAE launched a long-range sprint just before the two men were caught with 300m to go. Pedersen, of Trek Segafredo, rode the Colombian's slipstream and then went past like a slingshot.
He was chased across the line by Italian Jonathan Milan of Bahrain Victorious and Germany's Pascal Ackermann of Team UAE.
"It was pretty close in the end," said Pedersen. "It was not easy to catch them for a long time. All the sprint teams had to use all the guys we had available."
"I feel sorry for those guys because they did really, really well but I'm happy for the win."
Clarke, who was also chasing a first individual stage win in the Giro to go with Vuelta and Tour de France victories, said the finish was "devastating".
"Not nice to lose in that way getting caught so close," he said. "Would have preferred to be caught with 10k to go."
He brushed away suggestions that he and De Marchi should have kept working together.
"There has to be a moment when you have to decide to stop pulling."
Norwegian Leknessund, of Team DSM, stayed 28 seconds ahead of Belgian world champion Remco Evenepoel who started on Thursday despite falling twice in the rain the day before.
"Some pain in the back, some big bruises," said Evenepoel of Soudal Quickstep before the start. "I've got a big black spot on my back which is some blood."
After two days raced in pouring rain, the Giro briefly basked in the sunshine around Naples Bay with the blue flags of Serie A champions Napoli replacing the normal pink balloons along the route.
Rain is forecast to return for Friday's seventh stage, a 218km slog from Capua to the chilly heights of Gran Sasso, the tallest peak in the Apennine range.
