The 26-year-old Croat, a career-high eighth in the ATP rankings, beat Donskoy 6-3 3-6 6-3 to keep alive his chances of making it into the season-ending ATP World Tour Finals in London.
Second-seed Cilic, sixth in the race to London and needs to reach the final at this combined ATP and WTA event to increase his tally, broke his rival's serve early for a one-set lead in 40 minutes.
But in the second Donskoy also broke and kept his advantage through to level at one set all after one hour 16 minutes on court.
The rivals traded breaks early in the deciding set before big server Cilic produced the decisive break in the sixth game to take the set and the match in one hour 52 minutes.
"I'm pleased with today's performance as in the  opening match I always feel myself a bit rusty. Physically, I feel I'm pretty good and my top form is not too far away from me. It's just a matter of winning a couple of matches,” he said.
Seventh seed Mikhail Youzhny of Russia, the 2009 winner here, cruised comfortably into the second round past a compatriot qualifier Victor Baluda with a 6-3, 6-4 win.      

In the second round, Youzhny, who is 27th in the ATP rankings, will take on Argentinian Juan Monaco.
"We know each other pretty well as we've played many times including a very tight meeting last week in Shanghai," Youzhny said about his upcoming match with Monaco.
"He's currently in his top form and I expect a very interesting and tough battle on Thursday,” he added.
In the WTA section fourth seed Czech Lucie Safarova fired 15 aces and survived all seven break points in her first ever meeting with Croatia's prodigy Ajla Tomjanovic to record a 7-6 (7/4) 6-2 win.
"It was a good match for me as I was serving really well in both sets," this year's Wimbledon semi-finalist Safarova said.
"It was really close in the first set - the tie-break too - and I'm really happy I've got through my first round,” she added.
The 27-year-old Safarova will next face the fifth seeded local crowd's favourite Svetlana Kuznetsova, who battled back from a set down to beat Kateryna Kozlova of Ukraine 3-6, 6-3, 6-3.

Second-seed Ekaterina Makarova of Russia crashed out with a 6-4, 6-4 defeat at the hands of Romania's Irina-Camelia Begu.

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