Los Che, who finished third last season, were well worthy of a point and should have had three but Roberto Soldado's second half strike was incorrectly ruled out for offside.
Madrid, who have not made any new signings so far this summer, lined up largely as expected although Lassana Diarra was preferred to Sami Khedira and Higuain was chosen ahead of Karim Benzema.
In his first match in charge, former Los Che centre half Mauricio Pellegrino elected to start recently acquired trio Andres Guardado, Joao Pereira and Fernando Gago, with fellow new arrivals, Jonathan Viera and Nelson Valdez on the bench.
The champions made a bright start and after both Cristiano Ronaldo and Angel Di Maria came close early on, Higuain gave the home side the lead with just 10 minutes on the clock. A wonderful ball over the top of the Valencia backline from Di Maria found the Argentina striker, who, after being denied twice by goalkeeper Diego Alves, thundered a powerful effort into the top right hand corner from inside the area.
Against the run of play Valencia levelled four minutes before the break when Tino Costa's wonderfully whipped free-kick from the right was met by Jonas, who headed home. The Brazilian out-jumped Xabi Alonso, Pepe and Iker Casillas, with the latter two clashing heads. Both were left dazed by the incident, with Pepe needing a bandage to cover a gash and the Portuguese was replaced at the break by former Valencia defender Raul Albiol.
The home side were let off the hook when early in the second half a through ball inside his own half by Costa found an unmarked Roberto Soldado. The striker ran through the middle unchallenged before rounding Casillas and sliding the ball in the net only for play to be brought back for offside, although replays showed the 27-year-old was onside when the ball was played.
Substitute Benzema forced a good save from Alves with 10 minutes left, but Valencia were well worth a draw as the home side struggled to create chances.
Real Madrid coach Jose Mourinho was unhappy with the result.
"I expected more from my team. Last season when we drew 0-0 the best player for Valencia was Guaita (the Valencia keeper) and today it has been Alves, we did not play a great game but we did enough to win," said Mourinho.
Winger Cristiano Ronaldo was subdued throughout, and was also displeased with a draw.
"It's not a great result. We played well the first half and better in the second, we could have scored one or two more goals but we have to continue like that and we'll be ok," said Ronaldo.