The 25-year-old Konig, who rides for NetApp-Endura, also won a stage of the Tour of California earlier this month.
The ride that took the peloton along the southern coast and then up a steep mountain with spectacular views of the sea below shook up the top part of the overall standings after two days of tranquility.
Roche, the Irish SaxoBank-Tinkoff cyclist, opened up a 17-second lead over Moreno and American veteran Christopher Horner. Former leader Vincenzo Nibali ended up 18 seconds behind.
Former Vuelta winner Alejandro Valverde was 31 seconds behind in seventh place, while fellow Spanish favorite Joaquim Rodriguez was 1:03 back in 10th.
Roche, who won the second stage last Sunday, said he was surprised that he had taken the lead from Nibali.
"The other day when I attacked and got the win I missed getting the red jersey," Roche said. "I thought that if Nibali focused on other riders I could pick up a few seconds here and there and that's what happened today.
"Every year I come to the Vuelta with the dream of wearing the red jersey one day. It's incredible."
Garmin Sharp rider Daniel Martin abandoned the race before the day's start after falling on Friday.
Sunday's ride is a 163-kilometer (104-mile) mountainous stage from Antequera to Valdepenas de Jaen.
The three-week grand tour finishes in Madrid on Sept. 15.