Madrid recorded their fourth win in four Group B games, and their 12th consecutive victory in all competitions, beating Liverpool 1-0 at the Santiago Bernabeu thanks to a first-half Karim Benzema goal.
Meanwhile, Dortmund shrugged aside their dreadful domestic form to maintain their perfect record in Group D, crushing Galatasaray 4-1 in Germany.
Elsewhere, Atletico Madrid and Bayer Leverkusen won to close in on qualification for the last 16 while Juventus, Basel and Benfica all recorded precious victories but Arsenal threw away a three-goal lead to draw 3-3 with Anderlecht in London.
However, in the end the only goal of the game came in the 27th minute, Benzema converting a Marcelo cross at the back post. That meant Cristiano Ronaldo remains on 70 Champions League goals for now, one short of the competition record still held by Madrid great Raul.
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"I think we played well, albeit the tempo wasn't that high," said Ancelotti, while Rodgers praised Liverpool's display.
Liverpool are now three points behind second-placed Basel, who crushed Ludogorets Razgrad 4-0 in Switzerland with Breel Embolo, Derlis Gonzalez, Shkelzen Gashi and Marek Suchy on target.
Dortmund followed up a 4-0 win away to Galatasaray in Turkey two weeks ago by defeating the same team 4-1 in the return fixture with Marco Reus, Sokratis Papastathopoulos and Ciro Immobile all finding the target before a Semih Kaya own-goal late on, with Hakan Balta grabbing a consolation for the visitors.