Deportivo were left to rue two big opportunities missed by Florin Andone in the first 10 minutes, whilst the Romanian global also saw a late penalty saved by Keylor Navas.
The Spain defender was sent off in the closing stages of the game after picking up a second yellow card, after he caught Borja Valle with an arm during an aerial duel.
Those squandered chances proved costly when Madrid moved ahead in the 20th minute.
The home side were made to pay for those misses as Real soon took the lead after Ruben fumbled Luka Modric's shot from the edge of the box, allowing Karim Benzema to nip in and he quickly teed up Gareth Bale, who converted from close range.
Explaining the first incident with Schar, which occurred when Deportivo's Zakaria Bakkali player was injured on the floor, Ramos added: "We didn't kick the ball out because they didn't do it [earlier in the game]".
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The hosts nearly got one back when Guilherme turned in the box and fired a powerful effort against the crossbar.
- Sergio Ramos has equaled Xavi Aguado and Pablo Alfaro as the player with the most red cards in La Liga history (18).
- 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 Madrid ended the game as a contest just past the hour when Kroos found the back of the net with a powerful finish after Bale had delivered a low cross into the German worldwide.
- Keylor Navas has kept consecutive clean sheets for Real Madrid for the first time since November 2016 (all competitions).