Marcos Llorente thrived in midfield in Isco's absence but Madrid needed an eighth-minute intervention from Wass to take the lead on Saturday.
Dani Carvajal crossed from close to the byline on the right wing and Wass sent an attempted clearing header flying past goalkeeper Neto, while Thibaut Courtois was in fine form at the other end.
Vazquez – who also scored in the 2-0 win over Roma – slotted in the decisive second for Madrid with seven minutes to go, the goal surviving a lengthy VAR review, to claim all three points.
Madrid started well and took the lead in just the eighth minute, albeit in fortuitous circumstances.
Carvajal won back possession deep in the Valencia half and delivered a chipped cross to the front post that Wass could only guide into the roof of his own net.
Neto made a brilliant save to deny Gareth Bale and a long-range Dani Parejo shot was easily dealt with by Courtois.
Valencia should have equalised in the 53rd minute, Santi Mina racing onto an excellent Parejo ball over the top of the Madrid defence but hitting his shot too high to trouble the Belgium goalkeeper.
Another Parejo ball caused chaos in the Madrid box but, arriving at the back post, defender Gabriel was stretching and sent his volleyed effort flying over the crossbar.
Madrid almost extended their lead in the 72nd minute when substitute Marco Asensio was teed up by Llorente, Cristiano Piccini making a sensational block to stop the shot.
After Courtois brilliantly denied Michy Batshuayi, Isco was introduced for the last 10 minutes, with Karim Benzema then teeing up Vazquez for the clinching goal to ensure Madrid moved up to fifth in the LaLiga table.
What does it mean? Baby steps for Madrid
Last weekend's 3-0 loss at Eibar, after he won all four games as interim coach, showed Solari did not have a magic wand. But Madrid have now won back-to-back games without conceding and they are only three points off the top of the LaLiga table.
Llorente a pass master again
The absence of Toni Kroos and Casemiro due to injury has created an opportunity for Llorente and he has taken his chance with Isco out of favour. Having excelled against Roma, Llorente was terrific in midfield again and completed 95.2 per cent of his attempted passes, and 100 per cent in the opposition half.
Wass leaves Valencia a mountain to climb
There was some bad luck involved in Madrid's goal, but Denmark international Wass got himself in a poor position. The versatile midfielder deserves some sympathy, though, as he was being played in an unfamiliar full-back role by Marcelino, who has not won at the Bernabeu since 2006.
Real Madrid are at home again on Thursday when they welcome Melilla in the Copa del Rey, with Valencia hosting Ebro in the same competition two days earlier.