Deportivo nearly managed to pull one back late on but Florin Andone saw his penalty kick saved by goalkeeper Keylor Navas.
Deportivo continued to threaten, however, with Andone heading over the crossbar from close range in the 37th minute, while Bakkali was causing problems to the champions with his pace and trickery in a wide position.
Real Madrid's defender Sergio Ramos (R) clashes with Deportivo La Coruna's Swiss defender Fabian Schar during the Spanish league footbal match RC Deportivo de la Coruna vs Real Madrid CF at the Municipal de Riazor stadium in La Coruna on August 20, 2017.More news: Tropical Depression Eight forms east of the Bahamas
Depor's frustration grew when the Madrid captain then made a crucial goal-line clearance to keep out Andone's impressive header from Bruno Gama's cross.
But there was some frustration for Zidane, with Ramos, who had been fortunate earlier, dismissed in the second minute of added time after catching substitute Borja Valle with an arm in an aerial duel.
Ramos, 31, joins former Barcelona and Sevilla defender Pablo Alfaro and Real Zaragoza legend Xavi Aguado on 18 league red cards.
- There were 44 passes in the build-up for Casemiro's goal, the most before a goal in La Liga since at least 2006/07.
Real were without Cristiano Ronaldo, and will be for the next three games after his suspension in the Spanish Super Cup.