The 20-year-old Zverev became the youngest player to win a Masters 1000 event since Djokovic won in Miami a decade ago at 19.
"It's nice to know that I can compete and play and win the biggest tournaments on tour against the biggest players on tour," Zverev said.
Zverev broke in the very first game and was never really challenged by Djokovic, who appeared drained after having to win two matches a day earlier to reach the final.
"He's making his mark already," Djokovic said. "Today winning one of the biggest tournaments — absolutely deserved. Played great, served great. On the other hand, he didn't get much from my side. I played very poor today. Just couldn't find any rhythm."
Djokovic committed nearly twice as many unforced errors as Zverev — 27 to 14.
The match lasted 1 hour, 21 minutes.
Afterward, Djokovic announced that Andre Agassi will coach him at the French Open, which starts next Sunday.
"We are both excited to work together and see where it takes us," Djokovic said. "We don't have any long-term commitment. It's just us trying to get to know each other in Paris a little bit."
The title will move Zverev up to a career-high No. 10 in the rankings Monday and place him among the contenders for Roland Garros. It will also add credibility to the belief by many tennis experts that Zverev will reach No. 1 some day.
"If I have only half of the career Novak has had, I'll be fine," Zverev said when asked if he can follow in Djokovic's footsteps.
Tennis great Rod Laver presented Zverev with the trophy.
"Getting the trophy from Mr. Laver is something very special and something I'll remember for the rest of my career," Zverev said.
It was a tour-best fourth title this year for Svitolina and the most prestigious trophy of her young career. The 22-year-old Ukrainian also leads the tour with 31 match wins this season.
"Every day I'm just trying to work on my mental part, my physical, my tennis," Svitolina said. "Everything just came together and I'm very happy that it's happened in such a big tournament."
The fourth-ranked Halep was in full control and serving for the first set at 5-2 when she rolled her right ankle while sliding over what appeared to be a small hole in the Foro Italico stadium court.
While Halep was able to eventually win the opening set, she required treatment to her ankle from a trainer twice and was late getting to shots as the match wore on.
"Sorry guys for third set," Halep told the crowd. "It was a little tough for me to get through but Elina played great."
Halep was playing in her second clay-court final in two weeks after winning the title in Madrid last Sunday.
Svitolina also required medical treatment from a trainer midway through the second set, for an apparent problem with her left leg.
"Hopefully we'll recover, me and Simona, because we're struggling a bit physically," Svitolina said.
During the post-match presentation, Svitolina dropped the cover of the silver trophy on to the red clay court, prompting her to say, "Oops."
The first two sets featured long, nervous baseline rallies in which both players waited for their opponent to commit errors.
"It was very tough first two sets and I'm really happy that it's all finished," Svitolina said.
Andrew Dampf on Twitter: www.twitter.com/asdampf