A 24th-minute strike from Roksolana Kravchuk looked to have given the visitors victory in Glasgow, only for Harrison to glance home a header in the 93rd minute to earn a share of the spoils.
The point means the Scots remain second in Group B on ten points after four matches, six ahead of Ukraine, who have a game in hand over them. Leaders Spain have an 100 per cent record, having scored 35 goals and conceded none.
Despite home advantage, Scotland failed to take control of the opening stages and it was the Ukrainians who forced the first opportunities.
A mistake from Rachael Boyle allowed Olha Ovdiychuk a sight of goal, but her shot skewed wide. Then Veronika Andrukhiv was sent through on goal and as goalkeeper Lee Alexander narrowed the angle, she miskicked and the chance was gone.
The warning signs were there for Scotland, but they failed to heed them. Anna Petryk’s pass on 24 minutes was accurate but it should have been dealt with by Jen Beattie. However, the defender was too laboured in trying to intercept it, allowing Kravchuk to run on to the ball. She made no mistake, keeping her composure to fire past Alexander.
Scotland tried to respond and their best chance of the half came when Harrison broke free of the Ukraine defence, but her shot was too central and goalkeeper Daryna Bondarchuk parried.
Manager Pedro Martinez Losa hooked Beattie at the break, bringing on Sophie Howard for her, and the replacement nearly equalised, but her header went over the bar.
Caroline Weir then came so close, with her 20-yard effort cannoning off the crossbar via the fingertips of Bondarchuk.
Scotland continued to search for a leveller, with a deflected Erin Cuthbert effort skewing wide, but it was Ukraine who could have killed the game off had it not been for an excellent reflex save from Alexander to deny Tamila Khimich.
However, late into stoppage time, Boyle’s cross found Harrison and her header went into the net with the aid of the post.
Scotland are next in action on Tuesday when they take on Spain as they look to reach the finals in Australia and New Zealand.