The Spanish Under 21 international fed Karim Benzema for the 26th-minute leveller in Real's La Liga opener at the Bernabeu, and then rose to power a header under the crossbar four minutes from time for a 2-1 victory.
The diminutive playmaker is more noted for his ability with his feet than with his head, but broke through from midfield to head home from Marcelo's curling cross.
"It is the first header I have scored in La Liga and I'm delighted especially as it turned out to be the winner," the 21-year-old told Spanish broadcaster Canal Plus.
"It was important to win the first game at home. Betis surprised us a little bit but it is the first game of La Liga and we lack a little match-practice."
Isco appeared to be on the point of joining former boss Manuel Pellergini at Manchester City when he was signed by Real from Malaga two months ago.
He was a central figure as Spain won the European Under 21 championship in Israel in June, and has quickly become a popular figure among Madrid fans after some impressive performances during the pre-season.
The midfielder is on the fringes of Vicente del Bosque's senior Spain squad and is widely tipped to be in the running for a place at next year's World Cup finals in Brazil.
"The centre was superb and Isco's movement has been that of an expert at heading the ball," Real director and former striker Emilio Butragueno told Canal Plus.
"To give the pass for a goal and to score the winner, isn't a bad way to debut at the Bernabeu.
"I hope this is the start of a great era for him and Real Madrid. He is a different kind of player, and when he receives the ball everyone thinks something magical is going to happen.
"I am sure he will continue to develop."
(Reporting by Mark Elkington, editing by Pritha Sarkar)
