US Open champion Cilic is striving to secure a place in next month's season-ending ATP World Tour Finals and a 6-3 3-6 6-3 victory over Donskoy in the ATP 250 event in Moscow puts him a step closer to reaching the London showpiece.
Donskoy, playing in his home city, made the Croatian work for his place in the quarter-final, but the world number eight's class ultimately shone through.
Cilic sent down eight aces and broke three times to his opponent's two and will face either Tommy Robredo or Filip Krajinovic in the last eight.
Donskoy must have been fearing the worst when he lost his first service game to go 2-0 down, but the Russian showed plenty of character and it might have been a different story had he won a break point of his own to make it 4-3.
Cilic served out the set with minimum fuss, but world number 128 Donskoy claimed the only break of the second set to level the match.
A big upset looked to be on the cards when Cilic was broken in the first game of the decider, but he hit back straight away and claimed a decisive second break to go through.
Roberto Bautista Agut is also through to the quarter-finals at the expense of big-serving Australian Sam Groth, who was beaten 7-6 (7-5) 7-6 (7-4).
Groth clocked up 19 aces in a match that went with serve, but it was Bautista Agut who advanced as he won three points in a row to win a first-set tie-break and secured the decisive mini-break in the second.
Andreas Seppi, the eighth seed from Italy, was a 7-5 7-6 (7-3) winner over another big server in the form of Ivan Dodig.
Sixth seed Robredo and Mikhail Youzhny, seeded seven, were first-round winners against Pedja Krstin and Victor Baluda respectively.