The 37-year-old Serb won the opening 12 points of the center court clash against the 15th seed and was clinical throughout, apart from a minor lapse at the end of the second set.
Djokovic missed six set points as Rune briefly threatened to equalize late in the second set, but the result never looked in doubt.
Rune, 21, flashed flashes of brilliance that prompted chants of “Ruuune” from the evening crowd under the roof on another rainy day in south-west London.
But there were too many mistakes as he lost his 10th straight Tour match against top-five opposition.
Djokovic, who is aiming to equal Roger Federer’s eight Wimbledon titles, will face Australia’s Alex De Minaur in his record-extended 60th Grand Slam quarter-final on Wednesday.
