Louis Deletraz was running in second place and was on course for a strong points finish before a brake problem sent him spinning into the barrier at Turn 1 on lap 20.
After having difficulties on Saturday, Schumacher started the Sprint Race from 18th, but fought his way through the field over the course of the 28 laps to cross the line in fourth, right on the tail of de Vries as he searched for his maiden podium.
Schumacher takes his first points finish since the second race of the weekend in Baku. Behind Schumacher finished Saturday's Feature Race winner Nobuharu Matsushita.
De Vries took the lead of the race early on, but had a strange incident when his pit limiter became activated which saw him drop back to P6 and ruin his chance of a win.
The Japanese driver slipped down the order at the start as he was pushed wide at the exit of Turn 4, however he pushed through and made a late overtake on Nicholas Latifi to take seventh.
Zhou was in the fight for the podium positions early on, but slipped down the order as he struggled towards the end of the event.
Jack Aitken endured a nightmare race as he hit the rear of Anthoine Hubert while they battled for position at Turn 4. The crash destroyed Aitken's front wing, and saw him come home in 18th with a five second time penalty.
Bahrain International Circuit - Winter testing