Juve has made an unconvincing start to life under the legendary former midfielder and are four points behind Serie A leaders Milan after four games.
It was held to a 1-1 draw Crotone last time out but there was rarely any sign of a slip-up in its Group G opener, in which the Bianconeri, still without Cristiano Ronaldo, found little resistance from its host.
Morata, on target at the weekend, earned the three points with a simple finish in the first minute of the second half and a header six minutes from time, with the only blot on Juve's performance an injury to captain Giorgio Chiellini.
Federico Chiesa was Juve's most dangerous player throughout the first half and his arrowing strike drew Georgi Bushchan into an impressive diving save in the 12th minute.
Bushchan misjudged a corner soon after but Chiellini was unable to take advantage, drifting his header wide of the unguarded net.
Chiellini's evening was brought to a premature end when he limped off to be replaced by Merih Demiral, though Juve's rhythm was unaffected by that setback.
Indeed, Dynamo were grateful to Bushchan for maintaining parity 11 minutes before the interval as he kept out Dejan Kulusevski's flicked close-range finish after good work from Aaron Ramsey.
Ramsey and Kulusevski combined as Morata gave Juve the lead they deserved 49 seconds into the second half.
The former Real Madrid forward tapped in from point-blank range after Bushchan failed to handle Kulusevski's effort following neat build-up play from Ramsey.
Dynamo did attack with more energy in the closing stages but a scarcely deserved equaliser was not forthcoming and Morata made the game safe with a fine header from Juan Cuadrado's right-wing cross.