Schalke, now second in the German top-flight, took the lead just after break, with Yevhen Konoplyanka capitalising on an error from Marcel Schmelzer. A one-two allowed the Dortmund players to quickly close down the ball, but it was no use given the speed and accuracy of Naldo's sensational strike, his seventh league goal of the season.
"We have to make sure that at the end of the season we qualify for the Champions League, and I don't really care how that happens".
Victory saw Schalke pull four points clear of third place, while Dortmund drop to fourth.
"We made individual mistakes", Dortmund coach Peter Stoeger said after his second defeat in 15 games.
The Belgium worldwide has scored nine goals in 13 appearances, as Dortmund sit fourth in the Bundesliga table with four games of the season remaining.
Ralf Fahrmann was called into action for the first time on 24 minutes with a fine save to keep out Marco Reus' swerving free-kick, before Thilo Kehrer missed a good chance at the other end soon after when he failed to test Burki with a free header. The Dortmund captain lost the ball to Daniel Caligiuri, who surged forward and found the unmarked Konoplyanka to pick his spot and blast inside the left post. The defender hammered the ball past Dortmund's ineffective wall and inside the left post again.
Batshuayi has scored seven goals for Borussia Dortmund in the league since his loan move from Chelsea in January.
The local Ruhr Nachrichten newspaper reported the Belgian striker, who is on loan from Chelsea, is suspected to have suffered a lower-leg fracture.