The Trek Factory Racing rider was dropped by the peloton but fought his way back and eventually prevailed against Daryl Impey (Origa GreenEDGE).
Tosh van der Sande (Lotto-Soudal) came home third in the 173km stage from Andorra to Lleida.
“This was my first chance in this Vuelta," van Poppel said. "I missed the opportunities in the first week because I was not feeling good and struggled with the heat, and I was a little bit angry that I missed those chances.
"I knew that today was another chance, and I needed to take responsibility, and we as a team did it. It was a great job together.
“I felt really strong and then I know it’s hard to beat me on a little bit of an uphill. Especially also the guys, when I see the team pulling for me all day that really motivates me; it was really special.”
A five-man breakaway group took shape early on but they were reined in on the final straight after Giant-Alpecin had worked their way to the front of the peloton looking to set up a bunch sprint for John Degenkolb.
“Degenkolb took the wrong side of the road and I needed to go really early because I was a little bit in the back,” van Poppel said. “So I went full gas and I felt I had a lot of power in the legs and I came really easy over the guys and I won. I am really happy!
“I was a little stressed when I had the puncture because it was not far from the finish. But the change was really quick and I know that I am feeling really strong and sports directors Josu (Larrazabal) and Dirk (Demol) told me not to panic and be smart in coming back. By the time the team brought me back to the front the finale started immediately. It was perfect timing."
The general classification remained unchanged with Fabio Aru (Astana) holding the overall lead ahead of Joaquim Rodriguez (Katusha) and Tom Dumoulin (Giant-Alpecin) by 27 and 30 seconds respectively.
The stage started without Tour de France champion Chris Froome who abandoned the race after fracturing his foot following a crash in Wednesday's punishing mountain leg.
The 13th stage is a 178km mountainous ride from Calatayud to Tarazona, including the category 1 Alto de Beraton summit.
SBS will begin its live coverage of the Vuelta a Espana on Saturday 5th September with the 215km 14th Stage from Vitoria to Alto Campoo. SBS/HD and streaming online at Cycling Central from 2330 – 0200.