Sydorchuk, on target as a substitute in the 2-0 win away to neighbours Belarus on Thursday, finished off a swift counter-attack in added time at the end of the first half.
The speedy Evgeny Konoplyanka created the goal with a cross to the far post with Sydorchuk arriving to fire in from close range.
“We are happy with the result but not our performance. The final minutes were especially nervous. We should have scored a goal or two more to ease the pressure of the game in the end,” Sydorchuk told Ukrainian television.
The home side wasted the chance to double their lead two minutes into the second half when Andriy Yarmolenko smashed his penalty against the crossbar after Roman Zoulya had been brought down.
Macedonia's best chance fell in the opening 45 minutes to striker Adis Jahovic but he was denied by keeper AndriyPyatov.
The game was briefly halted in the final 10 minutes after a firework landed near to Macedonia keeper Tomislav Pacovski.
Ukraine, beaten 1-0 at home by Slovakia in their opening game, have six points from three matches.
(writing by Igor Nitsak; editing by Justin Palmer)
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