Morata galloped on to a Koke pass in the 28th minute at the Sanchez Pizjuan stadium in Seville and his shot took a slight deflection off a defender before looping over Ukraine goalkeeper Andriy Pyatov into the net.
The victory helped Spain maintain pressure on group leaders Slovakia, who won 3-0 at home to Luxembourg and have 15 points from five matches.
Spain, beaten 2-1 away to Slovakia in October, are second on 12 points, three ahead of Ukraine.
"It was a difficult game, they are very tough, very physical," Morata, who was playing in place of the injured Diego Costa, said in an interview with Spanish television.
"It wasn't my best game but now I just need to keep working to get another chance in the team," added the Juventus forward, who was making only his third appearance for La Roja.
Spain had the upper hand for most of the first half, with Andres Iniesta, David Silva and Isco at the heart of their forays forward.
Although chasing the ball for long periods, Ukraine managed to trouble the European champions and midfielder Ruslan Rotan lashed an effort narrowly wide moments before Morata struck.
Sergio Ramos nodded against the frame of the goal from a David Silva free kick and Spain goalkeeper Iker Casillas had to be alert to keep out a Rotan free kick either side of halftime.
Spain lost control in the second period as Ukraine pushed hard for an equaliser and the excellent Rotan twice tested Casillas with powerful efforts.
Spain substitute Santi Cazorla came close to a second for the home side three minutes from time but Pyatov pulled off a superb finger-tip save.
The next match for Spain, unbeaten in 30 competitive home games since they lost 1-0 to Greece in 2003, is a friendly on Tuesday against the Netherlands in Amsterdam, a repeat of the 2010 World Cup final.
(Writing by Iain Rogers, editing by Ed Osmond)
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