The 20-year-old surpassed Therese Johaug's record of four World Cup triumphs before turning 21 with victory in front of a home crowd.
Svahn edged out Russia's Natalia Nepryaeva by just 0.08 on the line to finish in 3:23.54s, with compatriot Jonna Sundling rounding off the podium 0.1 back.
The result saw Svahn swell her advantage at the top of the overall U23 standings and cut Lampic's advantage in the sprint category to just 20 points.
In the men's race, Paal Golberg saw off competition from Erik Valnes to secure top spot in a Norwegian one-two.
Golberg stopped the clock at 2:51.83s, with Valnes 0.52s behind and Russia's Alexander Bolshunov – leader of the general classification – coming home in third.
The 29-year-old's triumph sees him move third in the overall sprint standings, behind only Johannes Hoesflot Klaebo and Lucas Chanavat, with the former absent for Saturday's race.
Bradley Wiggins (Stage 20, 2012)
Greatest Tennis Players