Ricky Sbragia's side dominated much of the encounter at Burton Albion's Pirelli Stadium, but the game finished goalless. The Scots scorned a host of chances with Dundee United starlet Ryan Gauld particularly guilty.
But it was the United youngster who won the Scots a spot kick when he was tripped in the box. However, the penalty taken by Swansea City King's was tame and easily saved.
Now the Scots must raise their game when they face England tomorrow at the same venue, with the hosts opening their campaign with a 6-0 slaughtering of Montenegro.
Scotland missed a great chance in the 18th minute when Cammy Smith's cross was flicked on by Denny Johnstone, Liam Henderson left the ball for Gauld with only the keeper to beat, but the Dundee United wonderkid's effort was weak and straight at the keeper from 10 yards out.
Celtic striker Johnstone forced a save from Pidkivka and Gauld came close to making amends when he took hold of the rebound and skipped through only to be denied by a diving save from the busy Ukrainian keeper.
Scotland nearly paid for those misses before the break when Yevhen Chumak's free kick whizzed just wide before Roman Yaremchuk hit the post with a cross and Maksym Banasevych somehow volleyed the rebound wide right in front of goal.
Scotland spurned the best chance of the lot eight minutes after the break when King missed the penalty after Gauld was tripped by Pavlo Lukyanchuk as he darted into the box.
Scotland: Fulton; Sinnamon; Souttar, Hyam, McKenna; Henderson, Smith (Nicholson 66), Lindsay; King, Johnstone (Cardwell 46), Gauld.
Ukraine: Pidkivka; Kacharaba, Lukyanchuk, Polehenko, Tkachuk; Tankovskiy, Chumak (Kovalenko 61), Radchenko, Yaremchuk; Kharatin, Banasevich (Biesiedin 61).
Referee: M Gil (Spain).