Red Bull-BORA Hansgrohe rider Pellizzari attacked with 3.5km left of the 143.2km ride from O Barco de Valdeorras summit finish at the category one climb Alto de El Morredero and came in 16 seconds ahead of Britain's Tom Pidcock (Q36.5 Pro Cycling Team) with Australian Jai Hindley in third.
Vingegaard was next over the line, two seconds ahead of his closest general classification rival, Joao Almeida, and the Dane holds a 50-second lead, with Pidcock almost two and a half minutes down on the red jersey in third.
Pellizzari, fifth overall in his first Vuelta and wearing the white jersey for best young rider, found himself alongside the top four in the GC - Vingegaard, Almeida, Pidcock and Hindley -- along with American Matthew Riccitello (Israel-Premier Tech).
A battle between the top two may have been expected, but it was 21-year-old Pellizzari who made the decisive attack, and while Riccitello tried a couple of times to drag the others up to the leader, the Italian looked comfortable in winning his first Grand Tour stage.
"In the end, it's my fault for not getting on Pellizzari right away," a frustrated Riccitello said.
"But I really thought these other guys would want the stage win. Pretty disappointing that they didn't want to help, I don't think they had much to lose but that's bike racing."
An early 12-man breakaway was eventually reeled in before the riders reached the bottom of the final climb, and the race began in earnest as the main GC riders started to pull away.
Almeida looked to be struggling, dropped at one stage, but the Portuguese rider made his way back to stay in touch with Vingegaard, as these two look set to battle it out for the Vuelta win.
Pidcock, looking to hold on to third overall, made a sprint for the finish to take a couple of bonus seconds from Hindley, his main rival for the podium.
"I think that's the sacrifice, I guess, when riding for the podium," Pidcock said.
"I sacrificed the stage that could have been really nice. But, we're racing for the podium, that's the main goal so we have to make decisions."
Stage passes off without disruption
Before the race, riders voted to neutralise the stage if pro-Palestinian protests disrupted the race again, saying they had no intention of racing to an "undefined finish line", after the previous day's stage ended before the scheduled finish.
Tuesday's stage 16 was disrupted by protesters, a feature of this year's Vuelta, with stage 11 also coming to a premature end, but the main threat on Wednesday were strong winds at the summit finish, but in the end the riders were able to race to the line.
There were plenty of protesters present when the race passed through the town of Ponferrada with 25km to the finish, but police had the situation under control.
The area all around the finishing climb had been hit by fierce wildfires less than a month ago, and as the riders made their way up to the line they were greeted by charred barren hillsides.
Thursday's stage 18 is a 27.2km individual time trial in Valladolid which could be a flashpoint for further protests, after the Israel-Premier Tech team were stopped on the road by protesters during stage five's team time trial.