The Cambuur Stadion played host as Henk de Jong's side dominated the relegation-threatened Eagles but struggled to make the most of their advantage.
Their patience paid dividends, however, as Steblecki pounced with seven minutes remaining to keep their hopes of Europe alive.
It took 17 minutes for the clash to throw up a chance, and it came for the hosts as Mart Dijkstra drove a fine shot narrowly wide.
Go Ahead Eagles rode their luck to maintain parity at the break when they cleared another shot off the line, this time it was Dijkstra denied as the hosts went in frustrated at the break.
It was more of the same for much of the second half, until Steblecki turned home Wout Droste's cross to snatch the victory.