Alcaraz, who had an injury-plagued start to the season, came back in top form last month to win the Barcelona Open for the second consecutive year.
In Madrid, the Spaniard had to play his best tennis to beat a relentless Struff in three sets in a packed Caja Magica.
Alcaraz enjoyed a dream start to the match, breaking Struff’s serve in the first game. The German fought back to return the favour in the fourth but the Spaniard produced another break and closed the set 6-4.
Struff's aggressive returns helped him to rush to a 3-0 lead in the second set, which he took 6-3, but Alcaraz woke up in the third, breaking to lead 3-1 and taking the set 6-3.
"I have suffered more than I have enjoyed today but the finals are like that," Alcaraz said.
"There are times when your nerves get the better of you, your legs are heavy and it's difficult even though you want to play well.
"You have to be there all the time, Struff is very aggressive. I knew I was going to get bombs and I had to be prepared for it."
The victory was the fourth ATP Masters 1000 trophy for Alcaraz, who became the youngest world number one last September when he won the US Open.
