The French striker played at home for the first time in a Madrid shirt but was largely frustrated by Valladolid's defence.
Madrid midfielder Fede Valverde opened the scoring with a low deflected free-kick after 50 minutes and substitutes Brahim Diaz and debutant Endrick struck late on.
Madrid created little in the first half but did enough after the break to earn their first win of the season, following an opening draw at Real Mallorca.
Still lacking fluency in attack, Carlo Ancelotti's side stayed two points behind rivals Barcelona, who beat Athletic Bilbao on Saturday.
"We were too slow in the first half, the second half we were much more active, there was more movement, much faster with the ball," said Ancelotti.
Ancelotti brought in Arda Guler for the injured Jude Bellingham, expected to miss a month with a calf problem.
Real Valladolid were the only team in the division to keep a clean sheet in their opening fixture and from the start they set out to frustrate the champions.
Aurelien Tchouameni fired over from long range as Madrid dominated possession without threatening in the Spanish capital's summer heat.
Madrid came out with more bite in the second half and soon took the lead.
Valverde smashed home a vicious low free-kick with the help of a deflection to break the deadlock.
"It was very hard, above all at the start. We didn't click in the way the coach wanted us to, we lacked attitude when attacking, we were too passive and improved a lot in the second half," said Valverde.
"I'm very happy to help the team with goals but the important thing is the defensive work, of which I feel proud and these days I have to get involved in a lot."
Madrid should have doubled their lead but Rodrygo misplaced his pass with Vinicius waiting in the middle ready to score.
Mbappe chances
Mbappe blew a golden opportunity to get off the mark when Vinicius cut the ball across to him, but Estonian goalkeeper Karl Hein saved well.
The France captain had another chance on the counter-attack but fired wide before being replaced by 18-year-old Brazilian forward Endrick.
Mbappe made his dream switch to Madrid this summer at the end of his Paris Saint-Germain contract after years of links. He scored on his debut in a UEFA Super Cup triumph.
In La Liga, Mbappe has failed to score in his opening two matches as Ancelotti works on perfecting his set-up to get the best from the club's attacking stars.
The coach said Mbappe's role through the middle of the attack was not something he plans to change.
"He's a spectacular forward, very fast, moves well without the ball, attacks in behind, he had three or four chances (which were) created with his movement," said Ancelotti.
"In this position, he will score like he always scores, I don't think he needs to play from the left, in the centre in the end he will score goals."
Diaz secured Madrid's win with a neat lobbed finish after running on to a long ball from defender Eder Militao in the 88th minute.
In stoppage time the Spanish playmaker teed up Endrick who drilled home at the near post to celebrate his first appearance for the club in style.
"(Endrick) has got a lot of potential and for his goal he showed his quality," added Ancelotti.
"He's a centre-forward who plays in the box, in small spaces he's very dangerous."
Later Sunday, Atletico Madrid host last season's surprise package Girona among other fixtures.
