The world No.1 saved two break points at 4-4 in the first set and went on to win seven of the next eight games as he wrapped up a comfortable victory in 74 minutes.
No.3 seed Zverev started well but was quickly overwhelmed as errors started to dominate his game. The result combined with Marin Cilic's 6-7(2), 6-3, 6-4 defeat of John Isner later in the day, as Djokovic sealed his place in the semifinals at the for the eighth time.
"I don't think it was breathtaking tennis from both of us but a win is a win," said Djokovic, who hit only three winners in the first set compared to Zverev's 15.
"I started to play better in the second set and he was making a lot of unforced errors, which helped me win."
Djokovic entered the match having lost only one of his past 23 matches and started strongly, winning the majority of rallies from behind the baseline.
Zverev needed to serve well as he battled to stay in the set, hitting close to 80 percent of his first serves and firing seven aces. The German eventually forced the first break points of the match with the score level at 4-4 but Djokovic held after a backhand lob from Zverev drifted inches wide.
Errors were starting to creep into Zverev's game and his first serve percentage began to fall as Djokovic increased the pressure at 5-4. Zverev saved two break points before a double fault -- his 18th unforced error of the opener -- handed Djokovic the set.
The manner of Zverev's collapse set the tone of what was to follow. Djokovic continued to dominate on his serve and immediately pushed for another break, eventually finding the breakthrough in the fourth game to lead 3-1.
From there Djokovic won the next three games, dropping only one point, as he wrapped up his second win of the week.
It is not all over for Zverev who can still reach the semifinals for the first time if he beats Isner on Friday.
"I think I'll take it as a normal quarterfinal match at a normal tournament," said the German, who beat Cilic in his opening match on Monday.
"To be in the semifinals here would mean a lot to me. For that, I have to play good tennis."
Cilic kept his hopes of a semifinal berth alive as he came through this year's first three-setter -- improving his record at the tournament to a still dismal 2-9.
When he lost the first set to the American on a tiebreak it looked like more misery for Cilic, but he responded in superb fashion, even if he needed some help from Isner's mighty serve.
Isner double-faulted to hand Cilic a decisive break in the eighth game of the second set and then did the same to gift Cilic a break at the start of the third.
Isner said it had been "very very difficult" to focus on the match after learning of the death of his close friend and former strength coach Kyle Morgan.
Morgan, a 35-year-old former Florida University football player, was found dead on Monday after being reported missing by his family.
"Found out two nights ago after I lost to Novak," Isner, 33, told reporters after his defeat -- his second loss on his debut in the tournament. "It's difficult, very difficult. Got to go out there and play," he said.
Cilic wobbled briefly, handing the break back with a woeful game, but struck again with some bludgeoning groundstrokes and kept his composure to claim the win.
"There was a little bit of luck involved," said Cilic, who could have to beat Djokovic for only the third time in 19 meetings on Friday to progress.