Tchouameni added an extra dimension to the Real midfield and showed why they agreed to pay around €80 million to Monaco for the 22-year-old.
Real were in control until Joselu levelled from a rebound right before halftime and, roared on by their fans, Espanyol put up a fight against the European and LaLiga champions, dominating most of the second half.
Javi Puado almost put the home team in front after collecting a good pass inside the box, but his shot ended up being blocked by a defender for a corner.
In the 58th minute, goalkeeper Thibaut Courtois pulled off a fantastic one-handed stop to keep out Joselu's close-range shot.
Benzema had a great opportunity but was denied by keeper Benjamin Lecomte, put another effort wide, and had a goal ruled out by the video assistant referee (VAR) after a tight offside call.
Yet two minutes from time, Rodrygo found Benzema at the far post with a perfect cross and the France striker put Real Madrid back in front.
In added time, the VAR spotted a foul by Lecomte on Dani Ceballos in what was considered a clear goalscoring opportunity on the edge of the area.
Lecomte was shown a straight red card and Benzema took charge of the free kick, bending it into the bottom corner to wrap up the points.
"It was not easy and it will not be easy," Ancelotti said.
"We started very well, we scored but then we went down. After their goal, it was more complicated. It ended in a two-way match and we were very good.
"We were spot on with the changes we made. Rodrygo and Camavinga gave us the energy that we needed."