The 22-year-old from County Down in Northern Ireland finished on the same points (67) as Poland’s Pszczolarski, but edged ahead of him in the final sprint.
Holland’s Jan Willem Van Schip won with 104 and Spain’s Sebastian Mora Vedri took silver on 76.
“That means a lot,” Downey said. “I’ve had such a bumpy winter with a lot of crashes. I’ve finished fourth a lot of times in my career over this past year, I know what it’s like to finish fourth, so third there tonight is just a good as a win after so many emotions of being so close.
“It all flowed to me with eight laps to go. I was suffering so much, but I thought I can’t let that feeling happen again and to be on the other side of the coin is a very nice feeling.
“It was very hectic, but I knew it would be. I just had to bide my time. I split the race up into quarters.
“I played it smart, focused on the laps and didn’t get involved in the sprints because they’re not really my forte. It worked to my favour.”