Van Aert looked set to claim his second stage of this year's race in a fast finish in Seville but the 21-year-old Bittner (DSM-Firmenich-PostNL) edged out the Belgian on the line.
It was Bittner's first career win at a Grand Tour.
Van Aert (Visma-Lease a Bike) retained the points green jersey although he will rue a missed opportunity, as will Australia's Kaden Groves who was also looking for his second stage win of the race but had to settle for third place.
Slovenia's Primoz Roglic (Red Bull-Bora Hansgrohe) retained the overall lead after finishing safely in the peloton.
After the climbs of the previous day, Wednesday's 177-km stage from Fuente del Maestre to Seville was flat in comparison but still lumpy in the first half and ridden in fierce heat.
It was a day for a breakaway group and one duly materialised although when it was swallowed up with 38km still remaining everything boiled down to a bunch sprint through the Seville streets.
Van Aert launched his attack early and seemed to have done enough but misjudged his lunge to the line and Bittner took advantage to win by the narrowest of margins.
There was one casualty in the run-in as Portugal's Rui Costa (EF Education-EasyPost) was involved in a crash and was forced to abandon the race.
The Vuelta returns to the mountains on Thursday with race favourite Roglic holding an eight-second lead over UAE Team Emirates rider Joao Almeida.
