This match always looked like a potential banana skin for Real Madrid. With Cristiano Ronaldo still serving a suspension for pushing the referee in the Clasico at Camp Nou earlier this month and Sergio Ramos also banned, Los Blancos were without key men at both ends of the pitch.
Raphael Varane had been expected to make it, but ultimately missed out through injury and with Jesus Vallejo still sidelined as well, coach Zinedine Zidane was forced to pick Casemiro in central defence.
Valencia, a struggling side in recent seasons, also regularly raise their game for meetings with Madrid and had drawn four of their last six at the Santiago Bernabeu in La Liga. An improved team since the arrival of Marcelino Garcia Toral as coach in the summer, they gave Real a tough test.
But in Ronaldo's absence, Asensio stepped up. The 21-year-old opened the scoring as he controlled tha ball, ran through the middle of Valencia's defence and curled home with an exquiste shot into the corner with Neto well beaten.
The former Mallorca midfielder was all over the pitch as he helped out in defence, his first-half heat map showing he had spent a lot of his time in the right-back role as Valencia caused problems for the home side.
Late in the game, it was Asensio's intervention that rescued a point for Madrid as well, the youngster curling home a fantastic free-kick - only the second one he had ever taken for Real - to make it 2-2. And he almost grabbed a winner too, his shot blocked in the closing stages.
Either side of his two goals, Valencia scored twice themselves, through Carlos Soler in the first half and debutant Geoffrey Kondogbia in the second. The visitors also came close through Dani Parejo and saw a decent penalty appeal turned down.
In total, Valencia had nine attempts and converted two of those. Madrid, meanwhile, created enough chances to have won more than one game, but Isco, Gareth Bale and particularly Karim Benzema were wasteful in front of goal, firing high, wide and anywhere but on target as Real scored only two of 22 attempts.
Before kick-off, Madrid had been presented with their Liga crown some 98 days after winning the title in May and Cristiano was there to celebrate with his team-mates even though he was unable to feature in the match itself.
Ronaldo received the award for Best Player in Europe from UEFA as part of the Champions League draw on Thursday and the Portuguese was asked about the game's future stars.
“That is a very good question," he said. "I see some with great potential: Asensio, [Kylian] Mbappe, Neymar, [Ousmane] Dembele, [Eden] Hazard, [Marcus] Rashford ... and some others. In the next generation there are at least 10 players with very, very great potential.”
Asensio proved on Sunday night that he is indeed one of those and while both Bale and Benzema failed to shine and were whistled by the fans, the younger man delivered in spectacular style to show he looks like the best possible Ronaldo replacement right now - and perhaps even a worthy successor to the Portuguese in future.