Carlo Ancelotti's side were held to a 1-1 draw by Mallorca in their campaign opener, but they managed to post their first victory of the season here, with Valverde, Diaz and Endrick netting in the second half.
As expected, Real Madrid dominated the possession in the opening half of action, having 72% of the ball, but Los Blancos found it difficult to carve out opportunities.
Kylian Mbappe had the home side's best chance in the first period, but his 10th-minute strike was saved by Real Valladolid goalkeeper Karl Hein, and the visitors deservedly entered the half-time interval on terms.
At times, Real Valladolid were playing with seven across the back, but it was working, with Vinicius Junior and Rodrygo often coming into traffic when they should have been holding wide positions.
The home side managed to make the breakthrough early in the second period, though, when a short free kick outside the Real Valladolid box led to Valverde finding the bottom corner, albeit with the help of a slight deflection.
Arda Guler had been the player to benefit from Jude Bellingham's injury, with the Turkey international operating in the number 10 position, but he was replaced in the 69th minute of the contest by Diaz, who doubled Real Madrid's advantage in the 88th minute with a chipped finish after a long pass from Eder Militao.
Mbappe is still waiting for his first La Liga goal, but there was a special moment for Endrick late on, as the 17-year-old Brazilian capped his first Real Madrid appearance with a goal, finding the bottom corner with a low strike after breaking into the penalty box.
All three points were secured by Real Madrid due to their strong second-half display, with the reigning champions moving temporarily into third spot in the table.
REAL MADRID VS. REAL VALLADOLID HIGHLIGHTS
Federico Valverde goal vs. Real Valladolid (50th min, Real Madrid 1-0 Real Valladolid)
Real Madrid make the breakthrough in the early stages of the second period, as Valverde's strike from a short free kick takes a slight deflection before ending up in the bottom corner of the net.
Real Valladolid's resistance is broken after such a strong defensive display in the opening half of action.
88th min: Real Madrid 2-0 Real Valladolid (Brahim Diaz)
Brahim doubles Real Madrid's lead in the 88th minute of the match, as he collects a long pass from Militao before producing an excellent finish past goalkeeper Hein, who had vacated his goal.
Endrick goal vs. Real Valladolid (96th min, Real Madrid 3-0 Real Valladolid)
Endrick scores on his Real Madrid debut, with the 17-year-old picking out the bottom corner with an excellent strike after working his way into the Real Valladolid box.
MAN OF THE MATCH - FEDERICO VALVERDE
Valverde is far from the biggest name in the Real Madrid side, but there is absolutely no question that he is one of the first names on Ancelotti's team sheet due to his quality and work-rate.
The 26-year-old was the star of the show on Sunday, making three tackles during an excellent defensive performance, while he finished with a pass success rate of 93%.
Valverde was also the player to make the all-important breakthrough, with the Uruguay international's strike from outside the box ending up in the bottom corner, and it was a brilliant overall performance from the midfielder.
REAL MADRID VS. REAL VALLADOLID MATCH STATS
Possession: Real Madrid 67%-33% Real Valladolid
Shots: Real Madrid 15-6 Real Valladolid
Shots on target: Real Madrid 9-2 Real Valladolid
Corners: Real Madrid 5-5 Real Valladolid
Fouls: Real Madrid 9-15 Real Valladolid
BEST STATS
WHAT NEXT?
Real Madrid will be bidding to make it successive victories in Spain's top flight when they travel to Las Palmas on Thursday evening.
Real Valladolid, meanwhile, will look to build on what was a solid performance at Bernabeu for long spells when they continue their La Liga campaign at home to Leganes on Wednesday night.