There was a strong element of luck about Morata's 28th minute strike, the ball looping up off a defender and over the Ukraine goalkeeper into the net.
However, he had made a fine run into space to receive Koke's pass and held off his marker well to give himself the space to score his debut goal for La Roja on his third appearance.
"I am grateful that people say I am the future of the national team," Morata told reporters.
"I have to improve a lot of things and keep working and I am focusing on that so I can play well for my team (Juve) and when I come to play for Spain," added the 22-year-old.
The victory helped Spain keep up the pressure on Group C leaders Slovakia, who won 3-0 at home to Luxembourg and have 15 points from five matches with five games left.
Spain, who were beaten 2-1 away to Slovakia in October and host the eastern Europeans in September, are second on 12 points, three ahead of Ukraine.
Spain played well in the first half at Sevilla's Sanchez Pizjuan stadium and deserved their lead but Ukraine fought back strongly after halftime and had several chances for an equaliser.
The European champions will need to show more consistency if they are to have any chance of winning a third straight continental title in France next year.
"You can always improve," playmaker Andres Iniesta told reporters.
"Today we were really good in the first half but we struggled in the second," he added. "You always need to work and believe to get to the level you want."
Spain's next outing is a friendly on Tuesday against Netherlands in Amsterdam, a repeat of the 2010 World Cup final and their first meeting since Netherlands trounced Spain 5-1 in the group stage at the World Cup finals in Brazil last year.
(Writing by Iain Rogers, editing by Sudipto Ganguly)
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