The tone for a scrappy match was set early. Zverev started the match with two double faults to big cheers as he was broken in the first game before Alcaraz immediately gave the break back with a backhand error.
The Spaniard broke again to lead 3-2 and took his first set point after 43 minutes with a forehand cross court winner for another break.
Rome Masters champion Zverev, who had won his last 12 matches on clay, finally found his forehand and his confidence in the second set.
With the strong breeze whipping up the clay on the court, the German broke to lead 3-2 when Alcaraz framed a horrible forehand into the stand. The Spaniard gave up another break with a double fault to trail 2-5 before Zverev took his first set point with a forehand drop shot.
In the third set, Alcaraz clenched his fist to hold to lead 3-2 and then immediately broke to lead 4-2.