The Serbian world number one, who lost to Kohlschreiber at Indian Wells a year ago, was entirely dominant, sending down 23 winners and losing only 10 points on his serve as he wrapped up the win in 59 minutes without facing a break point.
"It was a great performance," Djokovic said in an on-court interview. "I enjoyed the way I played, coming out with the right focus and tactics."
Next up for the 32-year-old is a meeting with Russian seventh seed Karen Khachanov.
Djokovic breezes past Tsitsipas to claim fifth Dubai title
"I've had some interesting battles with him," Djokovic added. "He's a great guy, a very powerful player. He's one of the guys who is a pretender to be top five, top 10.
"He is very dedicated, so hopefully I'll be as sharp as I have been in the past two matches and start well."
Second seed Stefanos Tsitsipas of Greece also advanced to the quarters after beating Alexander Bublik of Kazakhstan 7-6(1) 6-4.
The match marked the second time in five days that Tsitsipas faced Bublik, who also lost to the Greek at last week's Marseille Open, where he successfully defended his title.
Tsitsipas will play Germany's Jan-Lennard Struff for a place in the semi-finals. Struff made short work of Nikoloz Basilashvili in their last-16 match, beating the Georgian 6-1 6-0 in 39 minutes.
Dan Evans pulled off the day's most dramatic escape in his round-of-16 meeting with Frenchman Pierre-Hugues Herbert, the Briton saving three match points in a third-set tiebreak before going on to win 7-5 3-6 7-6(7).
Evans next faces 22-year-old Russian Andrey Rublev, the sixth seed.
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