The unseeded 12-time Grand Slam champion produced a clinical display to win 6-4 6-1 and claim his first victory over a top-10 opponent since last May.
While Djokovic's dominance was based on his trademark pinpoint accuracy and elastic court-coverage, Australian Nick Kyrgios was at his idiosyncratic best earlier on a sunny centre court to beat home hope Kyle Edmund 7-6(7) 6-7(5) 6-3.
Kyrgios mixed brutal power with outrageous shot-making, sending down 32 aces and several between-the-legs specials to the delight of the crowd.
The 23-year-old will next face defending champion Feliciano Lopez in the quarter-finals.
Djokovic, ranked 22 after more than a year battling an elbow injury and indifferent form, arrived in London after a bitter end to his French Open hopes against unheralded Italian Marco Cecchinato, but has so far looked serene on the grasscourts.
He always looked in control against world number five Dimitrov and took the first set when he broke in the 10th game having gone 0-40 ahead on the Bulgarian's serve.
Dimitrov saved two set points but at 30-40 double-faulted to hand Djokovic the opener.
After that Dimitrov faded badly and Djokovic surged into a 5-1 lead before having difficulty clinching victory.
Three match points came and went but he converted the fourth when Dimitrov floated a sliced backhand long.
"Grigor made some crucial double faults today and that helped me take the first set. That first set was a huge confidence booster for me," Djokovic said on court after clinching his 799th career victory and seventh in eight against 2014 Queen's Club champion Dimitrov.
(Reporting by Martyn Herman; Editing by Ian Chadband)
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