The team from Deepdale ended a seven-match winless streak and reached 52 points, the same number as Swansea with a game in hand.
Stoke took the lead in the fourth minute with a goal from Sorbe Thomas.
Just ten minutes later Preston equalised through Alfie Devine.
Osmajić orchestrated a complete turnaround in the 57th minute after headed in a cross from Louis Dobbin, and just 180 seconds later he assisted Devin, who scored his second goal of the match for the final 3:1.
This is the eighth league goal of the season for the corpulent striker from Nikšić.
Another Montenegrin national team player, Andrija Vukčević, was substituted midway through the second half.
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