The 20-year-old forward bagged his first goal for Los Blancos with a late header that ensured his side took all three points after Xabi Alonso's penalty miss.
Cristiano Ronaldo gave the reigning Liga champions a first-half lead but Angel popped up with an equalizer midway through the second half.
It looked like Los Merengues were going to fail to pick up all three points away to Levante once more when Xabi Alonso missed from the spot but Alvaro Morata netted his first goal for the club when he headed in a late winner for the visiting side.
A waterlogged pitch made for a difficult start to the game and after one early shot, Ronaldo was forced to leave the pitch for treatment following a blow to the eye.
Levante pushed forward, eager to capitalize on the temporary numerical advantage but Juanlu was unable to convert the team's best opportunity as he blazed over from 10 yards out.
Given the dreadful nature of the pitch, both teams resorted to playing the long ball and it was perhaps predictable that the first goal would only come as a result of a set piece.
Sergio Ballesteros failed to deal with Alonso's dead-ball delivery and his header fell to Ronaldo who controlled with his thigh before lashing a volley into the roof of the net with 21 minutes played.
The weather continued to hinder the flow of the game and clearly content with the one-goal advantage, Jose Mourinho withdrew Ronaldo at the break and replaced him with Raul Albiol.
However, the change almost backfired immediately. Within two minutes of the restart the former Valencia man failed to close down Juanlu quick enough and his blushes were only spared by a magnificent stop from Iker Casillas.
Los Blancos soon settled again and started to threaten the Levante goal, hitting the crossbar twice before the hour mark.
Firstly, Pepe was afforded too much space from a corner but his header came crashing back off the woodwork. Then, as Munua failed to claim a corner from the right, Sergio Ramos' back heel was deflected onto the bar by Pape Diop before being sent behind for a corner.
But the profligacy of Mourinho's side came back to bite it as Jose Barkero's pass was flicked over the defense by Obafemi Martins. Substitute Angel got on the end of it, held off the challenge of Pepe, and lifted the ball over Casillas and into the net.
Madrid was offered a golden opportunity to take the lead in the 73rd minute as Ballesteros brought down Jose Callejon on the edge of the box and a debatable penalty was awarded. Alonso took on the responsibility of the spot kick but Munua guessed right and parried the shot aside.
Unperturbed, the home side continued to press and an error from Albiol was pounced upon by Juanlu. He picked up the loose ball and charged into the area but failed to pick out the far corner.
Yet there was to be one more twist in the tale in the 84th minute. Another quality free kick from Alonso found the head of Morata who nodded in the winner.
Despite taking the victory, Madrid remains eight points adrift of league leader Barcelona in third position.
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