Derby were in danger of being cut adrift before three pre-international break wins in a row lifted them off the foot of the Championship table and breathed life into their survival bid.
Their start at Pride Park against Preston reflected their confidence as they won a corner inside the first minute.
However, Preston, back in action after their FA Cup quarter-final exit against Aston Villa on Sunday, broke from it and had the game's first chance.
Nyambe's attempted backpass instead ended up being a through ball for Osmajic - but the Preston striker's first two touches took him slightly away from goal and he could only fire straight at Zetterstrom.
That was a let-off for Nyambe but he did not escape injury. The Rams right wing-back hurt himself in the process of trying to play the ball back and was forced off.
Derby then had another injury scare when their other wing-back, Callum Elder, was left writhing in pain after jarring his knee.
Thankfully for the hosts, he was able to run off the injury and return.
Once the game settled into a pattern, Preston dominated possession and could consider themselves unlucky when Osmajic put the ball in the net after the flag had already been raised against Ryan Porteous, who was deemed to have been offside before he flicked on.
However, replays showed Porteous was onside before his involvement in the move.