Gonzalo Meleros netted shortly after half-time restart to give Levante just their second win of the season at the Wanda Metropolitano.
It was a disastrous result for Atletico and one that saw them miss out an opportunity to climb back into the top-four.
The defeat could also give United an upper-hand mentally, with the Premier League club ending their run of bad results right in time for the European trip.
The Red Devils have been in disastrous form but finally got a win under their belt when they defeated Brighton 2-0 on Tuesday.
It was a welcome shot in the arm for United ahead of this weekend's trip to rivals Leeds and their European tie.
And Rangnick was delighted by Cristiano Ronaldo's performance against Brighton.
The Portugal superstar netted the opener before Bruno Fernandes wrapped up the points for United to kickstart their quest for Champions League qualification.
"That was an amazing goal," he said after the match. "Not only an important one but an amazing goal. I think overall it was a good performance by Cristiano.
"Energetically, he was on there, he was always trying to help the team-mates so I think in the last weeks definitely the best performance by him and a very, very important goal for us."