Portugal captain Cristiano Ronaldo ended a brief goal drought with Real's opening goal in the last 16, first leg in Gelsenkirchen and Brazil fullback Marcelo cracked in a second to put the La Liga giants within touching distance of the quarter-finals.
The comfortable victory helped dispel doubts about their form after they were knocked out of the King's Cup and thrashed 4-0 in La Liga by their city neighbours Atletico Madrid in recent weeks.
"We needed a game like that, with that kind of attitude and performance," Ancelotti told a news conference.
"And everything worked out well in the end," added the Italian, who led Real to a record-extending 10th European crown in his first season in charge in 2013-14.
"The team were serious and efficient and the opposition were pegged back from the start. Once we got the first goal, we controlled the game."
Real's next outing is a La Liga match at struggling Elche on Sunday, when Ronaldo will have a chance to show he really does have his scoring touch back.
The FIFA Ballon d'Or winner had drawn a blank in three consecutive matches before Wednesday and had come under fire for throwing a birthday party hours after the humbling La Liga reverse at Atletico.
"It's normal that when Cristiano scores 60 goals a season and then goes for three or four weeks without scoring people speculate that something's wrong," Ronaldo's Real and Portugal team mate Pepe told reporters.
"But I just focus on the work that he always does to help the team," added the centre back.
"He is like he always is. Happy, encouraging his team mates and that is what we ask for, that he transmits his happiness to the dressing room."
Real are a point clear of Barcelona at the top of La Liga with just over half the season played. Barca, who have a superior goal difference, can climb above their great rivals if they avoid defeat at home to Malaga on Saturday.
(Writing by Iain Rogers, editing by Sudipto Ganguly)
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