World champion Pedersen (Trek-Segafredo) outsprinted Pascal Ackermann (Bora-Hansgrohe) and Davide Ballerini (Deceuninck-Quick-Step) to claim victory and take the leader’s jersey.
The win came a day after Jakobsen was taken to hospital after a collision at the finish line with Dylan Groenewegen.
"First of all, I would like to dedicate this victory to Jakobsen after his crash yesterday," said Pedersen.
"I am super happy to dedicate it to him, [I wish] him a fast recovery, a comeback to life, to cycling. We had a strategy from the beginning that we should do the sprint for me.
"The team did a perfect job and I could finish it off. I don't know how it went behind me with Ackermann but it was just enough to keep him behind at the finish line. I am super happy to take the win in the jersey and show the team that I'm back in shape and back to racing strong."
Tour of Poland stage two highlights: Mads Pedersen wins sprint finish
Jakobsen (Deceuninck-Quick-Step), Groenewegen (Team Jumbo-Visma), Marc Sarreau (Groupama-FDJ), Eduard Prades (Movistar) and Damien Touze (Cofidis) did not compete in the stage after suffering injuries in yesterday’s crash.
Maciej Paterski (Polish National Team) and Julius van den Berg (EF Pro Cycling) formed a two-man breakaway that was caught with 16km remaining.
Then it was the turn of the sprinters, with Pedersen going first and managing to hold on for victory.