The relief was palpable on the face of 23-year-old when he broke the deadlock with a majestic header after the criticism he suffered for his performance against the Czech Republic.
"Two years ago, I was watching on the television and now I'm here," he said. "The most important thing about this group is the atmosphere and that is reflected on the pitch."
Even in their most triumphant years, Spain have struggled to find a centre-forward and during Euro 2012, they famously played without a recognised striker as Cesc Fabregas was deployed as a so-called "false No 9."
Since then, coach Vicente del Bosque has decided that he needs at least one forward but has struggled to find the ideal candidate for what is a notoriously difficult role in a team dominated by midfielders.
During the Euro qualifiers, Morata, Paco Alcacer and Diego Costa were all used but none did enough to win the position outright.
Alcacer finished as topscorer with five goals but missed the trip to France after a loss of form for Valencia, while Costa's below-par season for Chelsea and a hamstring injury in the run-up to the tournament cost the Brazilian-born striker his place.
Morata has played an important role for Juventus although his scoring rate is modest, with 12 goals in all competitions this season. But he is an unselfish striker who can dribble, lead counter attacks and hold the ball up.
Raised at Real Madrid, he was sold to Juventus two years ago although the Spanish side retained an option to buy him back.
He got off to an inauspicious start in Italy when he suffered a knee injury in his very first training session and was sent off in a fiery win over AS Roma in only his fourth outing.
But he quickly settled down and formed an excellent partnership with Carlos Tevez as Juventus won the league and Cup double and reached the Champions League final.
He clearly missed Tevez this season after the Argentine returned to play in his homeland but gave an outstanding performance in the Champions League match away to Bayern Munich and scored the winner in the Coppa Italia.
There has been speculation over a return to Real Madrid or a move the Chelsea but Juventus coach Massimiliano Allegri has warned that he needs to stay put to keep progressing.
"He's a young lad who needs to stay at Juventus for a few years, he still needs to grow," said Allegri. "I definitely want to keep Alvaro and the club agrees with me. We'll do everything to keep him, he must remain in Turin."
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