The Deceuninck-Quick Step rider edged out Bennett (BORA-hansgrohe) by a matter of millimetres in the flat finale to the 175 km ride along Spain’s east coast from Cullera to El Puig to earn his first-ever victory at a Grand Tour.
The stage, which contained only one classified climb and had a 20km flat finish, was one of the more straightforward routes of this year’s Vuelta and was always going to favour the sprinters.
“To win in a Grand Tour is one of the things you dream of as a sprinter," Jakobsen said. "I came to the Vuelta as a 22-year-old to learn and to try and win.
"In my head, I thought I could do it, but you never know for sure. To win a stage of La Vuelta wearing the colours of your country is amazing.
"Yesterday, maybe we were a bit too nice. This time, we took the initiative. [Remi] Cavagna was very strong and even made a gap in the final. I stayed behind [Zdenek] Stybar and [Maximiliano] Richeze.
"They are the best in the world at what they do, and they set me up in a perfect position for the final 200 meters."
Bennett, who picked up a fourth Grand Tour stage win the previous day — his first at the Vuelta — looked to be on course for a stunning repeat victory but his decision to take a right turn rather than left at a roundabout as the final kilometre approached saw him lose valuable position.
He recovered in the last stretch of the stage but narrowly failed to unseat Jakobsen.
“Disappointed to take second place but genuinely delighted for Fabio on his first Grand Tour stage win," Bennett said.
"Unfortunately, everything that could go wrong went wrong in the final. I lost maybe five positions when I went the long way around the roundabout and had to really fight to get back up to the leading positions.
"Our riders had already made a huge effort working to pull the race back so my thanks to them for that, it simply meant I was fighting for myself to get on the right wheel and I simply ran out of metres. The legs were great so we'll fight again."
Nicolas Roche (Sunweb) holds a two-second lead in the general classification over second-placed Nairo Quintana (Movistar) while Rigoberto Uran (EF Education First) is third at eight seconds despite being involved in a minor crash during the stage.
The Vuelta lost another high-profile name earlier in the day when Steven Kruijswijk (Jumbo-Visma) withdrew from the race with a sore knee which had become aggravated after a crash in the opening team time trial.
Stage five is a 170km hilly ride from L’Eliana to Alto de Javalembre containing three classified climbs and is the first of eight summit finishes at this year’s race.