He did not drop a set in his first Eastbourne appearance and the 12-time Grand Slam champion eventually secured a 6-3 6-4 win.
The Serbian world number four will play Russian Daniil Medvedev, who beat American fourth seed Steve Johnson 6-3 2-6 6-3, on Friday for a place in the final of the south coast grass tournament.
He suffered a surprise early exit to Sam Querrey at Wimbledon a year ago, then was beaten by Swiss third seed Stan Wawrinka in the US Open final.
Top seed Djokovic, playing in his first Wimbledon warm-up event since 2010, will be seeking his first title since claiming the Qatar Open in January.More news: Russian, Ukrainian companies' websites under massive cyber attack
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It is the first time that Djokovic has played at Eastbourne, a sign of how seriously he is taking his Wimbledon preparation after a tough 2017. "This is the kind of match situations that I was looking forward to having, and I'm glad it happened today and I managed to overcome that".
Karolina Pliskova gave herself the ideal pre-Wimbledon tonic by lifting the women's title, defeating Caroline Wozniacki 6-4, 6-4 in impressive style. It just didn't feel quite right. A similar pattern developed in the second, another early break leading to another 2-0 lead.
With world number one and two Andy Murray and Djokovic both struggling with form and Nadal fearing whether his injured knees will bear the pain and stress of the grass courts, Federer is all but set to go into the tournament as the favourite contender. "Next week is Wimbledon but I make decisions for my health", said Konta. I was also in final.
Croatian Ancic is only three years older than Djokovic at the age of 33 after being forced to retire due to injury in 2011.