The 21-year-old Czech rider took the challenge to the sprinters at the end of a flat 177km run from Fuente del Maestre to Seville, edging Belgian star Van Aert to the line.
"It's unbelievable," Bittner told Eurosport. "Only a few days ago I got my first pro win, so to get my first win at my first Vuelta, I still can't believe it.
"To beat Wout van Aert, one of the best long sprinters in the world, is just crazy. I told the guys today that we could do it and I really believed in it. When the opportunity came, I really went for it, full gas."
Primoz Roglic remains in the leader's red jersey as he seeks a record-equalling fourth Vuelta title. Van Aert is in green as the sprinter with the most points.
Roglic, who won the first mountain stage on Tuesday, leads Joao Almeida by eight seconds overall. Enric Mas is third at 32 seconds.
The peloton heads back into the mountains on Thursday for stage six, which features four categorised climbs along the 185.5km route between Jerez de la Frontera and Yunquera.
