Diego Simeone's side had gone four home matches in all competitions without a win and had only scored once in its past three games at Wanda Metropolitano.
They rarely looked like ending that particular run against a Leverkusen side who lost their first two Group D matches and were beaten 3-0 by Eintracht Frankfurt last Friday, until Morata's powerful 78th-minute header proved too much for Lukas Hradecky.
Atletico lost Jose Gimenez to injury after only 15 minutes but Jan Oblak's goal was relatively untroubled, despite the visitors enjoying most of the first-half possession.
Hradecky made a routine stop from a Renan Lodi shot but Simeone's forward line seemed blunted without the injured Joao Felix, with Diego Costa's frustrations compounded when he went to ground easily under pressure from Mitchell Weiser and failed to win a penalty.
Simeone threw on Morata for Koke with 20 minutes left in a bid to spark life into the attack, and the former Chelsea striker made a swift impact when he pressured Hradecky into clearing a simple ball out of play.
And Morata made the all-important breakthrough, heading home only his second goal of the season from six yards out after meeting Lodi's cross from the left.