Real took their revenge against the Moldovan side, who pulled off a shock 2-1 win in the reverse fixture in September, with goals from defender David Alaba, midfielder Toni Kroos and striker Karim Benzema enough to claim the victory.
Alaba scored his first Champions League goal in six years to put the visitors ahead in the 30th minute before Kroos doubled their lead with the last kick of the first half.
Benzema added the extra in the 55th minute to secure the win for the Spaniards and solidify their place at the top of Group D.
"We played a good game, a serious game from the start," Real manager Carlo Ancelotti said. "They pushed at first but we controlled them and then we controlled the ball, we carry on with a good dynamic, we keep moving forward."
"I said at the start of the season, this team can compete. Things are going well, we're showing a lot of quality in various sectors and various players. Today the team played seriously, played good football."
Kroos, who was named UEFA's Man of the Match for his impressive goal and impactful performance, was praised by Ancelotti after the game.
"If Kroos is well, the coach is calmer!" he said. "He controls the ball like nobody else. In recent games he's scored goals too, he's doing well."
Sheriff goalkeeper Georgios Athanasiadis pulled off several stunning saves throughout the match to keep the scoreline to three, but the loss sees the Champions League debutants drop into the Europa League.
Real were dominant throughout the game, looking confident from the whistle.
Benzema appeared to put the visitors ahead in the ninth minute after he took advantage of a weak save from Athanasiadis and slotted the rebound into the net, but he was immediately ruled offside.
The deadlock was eventually broken in the 30th minute, Alaba putting the visitors ahead after his free-kick attempt was deflected into the net.
Kroos then doubled Madrid's lead on the stroke of half-time, the ball fizzing off the underside of the bar over the line.
After a strong run of play from the Spaniards, Benzema added a third on the 55th minute from outside the box after being set up by Ferland Mendy.