Jakobsen (Deceuninck-QuickStep) won a dramatic sprint to claim the narrowest of victories in El Puig, after Bennett had made an impressive recovery from taking a wrong turn around a roundabout.
Germany's Maximilian Walscheid (Team Sunweb) was third while his team-mate Nicolas Roche from Ireland retained the overall leader's red jersey.
Roche maintained his lead over his two Colombian chasers, with Nairo Quintana (Movistar) two seconds behind and Rigoberto Uran (EF Education First) a further six seconds back.
Jakobsen picks up his first grand tour victory in his debut appearance at the Vuelta after another relatively flat, 175.5-kilometre stage, that was always likely to play to the sprinters.
"I don't know how close it was, maybe a couple of millimetres," said Jakobsen "I just threw my bike at the line."
"I knew (I had won) when I saw guys from team cheering," he said. "I couldn't see because I had my eyes closed."
Jelle Wallays (Lotto Soudal) and Jorge Cubero (Burgos-BH) were the early escapees and even stretched their lead over the peloton to seven minutes with 139km left.
But soon after the category three climb of Puerto del Oronet, Cubero was hit by a mechanical problem before Wallays was caught by the peloton with 18km remaining.
Bennett's costly mistake came with just over 5km to go as he went right around the penultimate roundabout, losing precious time on the leaders.
Max Richeze led out the sprint, with his team-mate Jakobsen close behind, only for Bennett to weave through the pack in a late surge for the line. A photo finish showed Jakobsen had held on.
Stage five on Wednesday, between L'Eliana and Observatorio Astrofisico de Javalambre, offers the race's first summit finish and offers the biggest test so far of those hoping to win the general classification.
Earlier, Steven Kruijswijk, one of the event's leading contenders, was forced to pull out with a knee injury sustained in a crash in Saturday's team time trial.
Kruijswijk's team, Jumbo-Visma wrote in a statement that the rider "has abandoned the Vuelta. He's suffering a sore knee due to the crash in the TTT and the pain has gotten worse."
Vuelta a Espana fourth stage results on Monday, 175.5km from Cullera to El Puig:
1. Fabio Jakobsen (NED/DQT) 4hr 4min 16 sec, 2. Sam Bennett (IRL/BOR) s.t., 3. Maximilian Walscheid (GER/Sunweb) s.t., 4. Fernando Gaviria (COL/UAD) s.t., 5. Luka Mezgec (SLO/MIT) s.t., 6. Marc Sarreau (FRA/GFC) s.t., 7. Szymon Sajnok (POL/CCC) s.t., 8. Edvald Boasson Hagen (NOR/TDD) s.t., 9. Jon Aberasturi (ESP/CJR) s.t., 10. Juan Sebastian Molano (COL/UAD) s.t.
1. Nicolas Roche (IRL/Sunweb) 13hr 55min 30sec, 2. Nairo Quintana (COL/MOV) at 2sec, 3. Rigoberto Uran (COL/EF1) 8, 4. Mikel Nieve (ESP/MIT) 22, 5. Miguel Angel Lopez (COL/AST) 33, 6. Primoz Roglic (SLO/JUM) 35, 7. Sergio Higuita (COL/EF1) 37, 8. Wilco Kelderman (NED/SUN) 38, 9. Davide Formolo (ITA/BOR) 46, 10. Rafal Majka (POL/BOR) 46.