Karim Benzema put Madrid in front midway through the first half with a fine finish and a deserved lead for a visiting side that dominated possession throughout the minutes leading up to the goal.
Valencia drew level with a Soler penalty on his second try after seeing his initial attempt saved, but converting his second effort after VAR ruled that players had come into the area before Voler's first try.
The hosts then took the lead thanks to a Raphael Varane own goal to go into half-time with a 2-1 edge.
"It's great to finally get the rewards of all the hard work we have been putting in recently without getting the results we deserved," said Valencia coach Javi Gracia.
"I always felt we were competing well even if results weren't going our way and we need to keep going down this path. This result will strengthen our belief in what we are doing and give the players confidence for the games ahead."
A questionable penalty call against Marcelo handed Valencia another chance from the penalty spot and Soler stepped up to dispatch his second spot kick of the night and double Los Che's lead.
VAR then awarded Valencia a third penalty for handball on Sergio Ramos and once again Soler was up to the taks, netting his third from the spot on the day and staking his side to a 4-1 lead.
Soler became only the third player in the history of La Liga to score three penalties in a single match
The loss sees Zinedine Zidane's side stuck in fourth place in La Liga with 16 points through eight games played.
After the match, Zidane said: "We started the game well, the first half hour, after the goal we dropped off and changed the dynamic. That could be a problem. Then a bit of everything happened, we had the three penalties, an own goal. Today it's difficult to understand our game. We started well and after they equalised, everything changed.
"There's no justification, no excuses. The game changed. We started well, the first half hour, then we dropped off. Three penalties, everything came together today against us, it's a bad game and a bad day."