Bjoergen, who turned 33 on Thursday, had to settle for second in the opening sprint in Stockholm on Wednesday as World Cup champion Kowalczyk finished first for the lead.
Kowalczyk had a cushion of 7.1 seconds over Kerttu Niskanen and 8.4 over Bjoergen heading into the 2.5km freestyle individual prologue. However, she was to finish well down the field.
Bjoergen comfortably made up her deficit to clock the quickest time, 6:03.2, while Kowalczyk was almost 11 seconds off the pace as he placed fifth in the prologue.
Swedish home hope Charlotte Kalla was the second fastest, 4.4 seconds slower than Bjoergen, while Kikkan Randall was third another 2.2 behind and Astrid Uhrenholdt Jacobsen fourth by another 0.5.
Bjoergen now leads Kowalczyk by almost 18 seconds in the mini tour standings with Kalla almost another seven behind in third with the 10km classic mass start next up on Saturday.
And Bjoergen, who won four golds and a silver at the World Championships in Val di Fiemme, admits she will have to be at her best to defeat Kowalczyk once again.
"It was a good day. The race fit me very good, my legs felt good and I tried to push hard. I was a little bit slow downhill but it was OK and I pushed coming into the stadium," said Bjoergen.
"I will try hard for the next race. Justyna will go hard and I will try to follow her and Therese Johaug. My body is feeling and everything is possible."