Giant-Shimano sprinter Degenkolb stayed in touch with the main pack over two testing climbs during the 165km stage from Mairena del Alcor to beat Spaniard Vincente Reynes (IAM Cycling) and Orice-GreenEdge's Matthews in a rather muted bunch sprint.
Four bonus seconds for third place saw Matthews extend his race lead to eight seconds over Colombia's Nairo Quintana (Movistar).
Quintana's team-mate Alejandro Valverde attacked near the summit of the final climb inside the final 25km to join three riders - including Britain's Adam Yates of Orica-GreenEdge - off the front of the race.
The attack was neutralised after a fast descent with 10km remaining as the teams of the main favourites Degenkolb and Matthews came to the front of the pack.
With temperatures soaring above 40-degrees, many riders had fallen by the wayside - including out-of-sorts Peter Sagan (Cannondale) and stage two winner, the green jerser Nacer Bouhanni (FDJ).
Reynes launched his attack early but the Spaniard was no match for Degenkolb who powered clear on the home straight to win by a few bike lengths.
"I love the Vuelta a Espana and also the country. I'm always happy to be here - I love the Spanish lifestyle and the food," Degenkolb charmed reporters after ensuring his Giant team have now notched stage wins in the last seven Grand Tours.
"Yesterday was disappointing not to hang on in a hard and explosive finish and I always need one or two days to adapt to the heat.
"But today I felt much better. My team did a great job to get me there and it's always a good feeling to win a stage on the Vuelta," said Degenkolb, who notched five stages in his breakthrough race in Spain in 2012.
FOUR-MAN BREAK: The day's main break of Javier Aramendia (Caja-Rural), Gert Joeaar (Cofidis), Sebastien Turgot (Ag2R-La Mondiale) and Jimmy Engoulvent (Europcar) opened up a maximum lead of four and a half minutes before wilting in the heat on the Cat.3 Alto di San Jeronimo.
Turgot was first to be caught before Aramendia and Joeaar were reeled in just before the summit. Another Caja Rural rider, Amets Txurruka, attacked from the pack to join Engoulvent on the descent, the pair opening up a gap of 45 seconds before fading fast.
With Tinkoff-Saxo setting a fast pace on the downhill, the peloton blew to pieces and multiple groups soon formed - with Carlos Betancur (Ag2R-La Mondiale), Thibaut Pinot (FDJ), Fabian Cancellara (Trek) and Sagan all among a flurry of riders to feel the pinch.
The Sky team-mates of Britain's Chris Froome took over the baton on the Cat.2 ascent of of Catorce por Centro to whittle the pack down to around sixty riders.
Colombia's Winner Anacona (Lampre-Merida) and British youngster Adam Yates (Orica-GreenEdge) attacked near the summit inside the final 30km, soon to be joined by Frenchman Romain Sicard (Europcar) and that man Valverde.
But the move was as ambitious as Giant and GreenEdge's combined hunger for a bunch sprint was large, the race coming back together for a restrained run into Cordoba ahead of Degenkolb's routine win.
RIDE OF THE DAY: Despite his hefty build, 25-year-old Degenkolb managed to stay near the front on both climbs and still had the energy to soar past his rivals on the finish straight - a classy display from the German powerhouse.
DAY TO FORGET: Peter Sagan struggled once again in the heat, with Eurosport commentator Sean Kelly remarking that the advertising across the back of his shorts was much more legible because of the kilos the Slovak had put on since the Tour. Too busy celebrating your move to Tinkoff-Saxo with Champagne and caviar, eh Peter?
COMING UP: Wednesday's 180km stage from Cordoba to Ronda features a Cat.3 climb 15km before the finish ahead of another finish with a slightly uphill kick. Both Matthews and Degenkolb will fancy their chances in doubling up.
Stage Four result
1. John Degenkolb (Germany / Giant) 4:02:55"
2. Vicente Reynes (Spain / IAM Cycling) ST
3. Michael Matthews (Australia / Orica)
4. Damiano Caruso (Italy / Cannondale)
5. Daniel Martin (Ireland / Garmin)
6. Alexandr Kolobnev (Russia / Katusha)
7. Lloyd Mondory (France / AG2R)
8. Valerio Conti (Italy / Lampre)
9. Bob Jungels (Luxembourg / Trek)
10. Fabio Aru (Italy / Astana)
- Sports & Recreation
- Peter Sagan
- Adam Yates