The hosts made eight changes to their side for the game and there were signs of ring-rust at both ends of the pitch as they made heavy going of beating the former European Cup finalists.
Maurizio Sarri's men dominated the ball for long spells, but struggled to put the finishing touches to moves as Morata in particular suffered a largely frustrating evening.
Emerson Palmieri was game in attack throughout and arguably could have done better after dancing away from several challenges and into the box with 10 minutes on the clock, only to blaze over after bursting into the box.
It was Morata who would have and ultimately waste the best chance of the first half, though. The Spaniard inexplicably missing the target after being slipped in one-on-one by Pedro's wonderful reverse ball.
That aside, Chelsea's main attacking threat came from long-range efforts, with Willian, Pedro and Mateo Kovacic all trying, and failing, to find the breakthrough.
The visitors came into the game slightly more as the half wore on, with the speedy Loic Nego causing Emerson some problems in defence.
First, he almost embarrassed Andreas Christensen by getting in between him and Kepa Arrizabalaga as the Dane attempted to shepherd the ball back to his goalkeeper, but he was unable to guide his prodded effort on target.
Then, on the stroke of the break, the Frenchman found himself in a wonderful position having brushed Emerson off the ball and jinked past Christensen in the box. However, he opted to shoot when he had two players in support and his tame left-footed effort was easily kept out by Kepa at the near post.
With that the two sides went in level and after Nego called Kepa into action immediately after the restart Sarri soon turned to his bench to introduce Eden Hazard.
Georgi Milanov and Ruben Loftus-Cheek both cleared the crossbar, before the hosts finally made the breakthrough with 20 minutes to go.
Having missed a sitter in the first half and clashed with veteran defender Roland Juhász throughout, it was only right that Morata was the man to score what would prove to be the winner.
Cesc Fabregas was given time and space out on the right to measure a pass and he clipped the ball onto the head of Willian, with the Brazilian alert enough to flick the ball into the path of Morata, who made no mistake this time as he prodded home from six yards.
Substitute Ross Barkley went close to doubling the lead minutes later as his flicked header from a Willian free-kick bounced back into play off the woodwork, though Vidi did have one late chance to snatch an unlikely point as István Kovács was slipped in behind a sleeping Cesc Fabregas, the Hungarian forcing a sharp low save from Kepa with the outside of his foot.
Morata drove across the face of goal at the death but he was unable to add to his and Chelsea's tally as the 'Blues' emerged 1-0 winners for the second European game in succession.
The win leaves Sarri's side top of Group L after BATE's defeat to PAOK in the night's other game, whilst MOL Vidi remain bottom having yet to get off the mark.
October 4, 2018