Serving for the set, Marozsan served two aces to lead 30-0.
Alcaraz netted a down the line backhand return to face set point.
The 23 year old Marozsan served and volleyed on set point; striking a crosscourt swinging forehand volley winner to hold serve and take the set after only 32 minutes of play.
At 3-3 in set two, Alcaraz dropped serve following several groundstroke errors to trail 3-4.
Then with Marozsan serving down breakpoint, Alcaraz struck a dropshot which he followed up with a crosscourt passing shot winner to break serve and level the set at 4-4.
The set then remained on serve to reach a decisive tiebreaker at 6-6.
Alcaraz took a 4-1 lead before Marozsan struck several powerful forehand winners including an 86 miles per hour inside out forehand down the line winner to lead 5-4.
Alcaraz struck a down the line forehand wide while on the run to trail 4-6 and face match point.
The six feet four inches tall Marozsan struck one final powerful inside out forehand down the line.
Alcaraz returned it in a crosscourt forehand which landed long to end the match after one hour and 40 minutes of play.
Marozsan, who only lost serve once for the day, won the last six points of the match.
"I just didn't feel comfortable. He made me to feel uncomfortable on court," Alcaraz said.
"He was aggressive all the time. He was playing inside the baseline all the time. It was tough for me to get into the match, into the rally. I made a lot of mistakes that I usually don't make too much."