Djokovic secured that game with a forehand victor, then saved two game points on Nishikori's serve before converting his first match point with a forehand down the line.
When Anderson broke again in the fourth, Federer was suddenly on the ropes. "Maybe I don't have good results or good record with him, but I always enjoy playing him". The level of tennis has been going up in the past couple of months and tournaments.
"I am very grateful to play on the court I love [Centre Court] and to be competing at a high level".
"It's one of those average days you have to try to win the match, and I just couldn't get it done today".
Djokovic looked in control in the first set.
A nagging elbow injury caused him to take an eight-month break from the sport prior to last year's US Open, and he also admitted to having to deal with personal issues. Croatia's reward for ending Russian hopes is a Wednesday semi-final in Moscow against England.
Novak Djokovic is feeling more optimistic after continuing his fine run at Wimbledon by reaching the quarter-finals. Scot Murray, 32 - who triumphed here previous year alongside Martina Hingis - and former singles world No.1 Azarenka moved into the quarter-finals with a 7-6 (8-6), 6-3 win over Matwe Middelkoop and Johanna Larsson.
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Soon afterwards the USA sent about 100 coffins to Panmunjom to put the remains into, but they have been sitting there ever since. According to estimates from the Pentagon, 7,700 US troops are still unaccounted for from the Korean War.
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At the start of the second, Djokovic was putting Nishikori under vast pressure again, but the Japanese held firm on serve in a 10-minute game. "His consistency, the way he plays such great tennis week in and week out", said Anderson. Ramos then hit Djokovic with a time violation warning for taking too long to serve in the seventh game of the fourth set.
He had a break opportunity as Nishikori opened set two but squandered the chance and the Japanese broke the Serb's resistance for a 3-1 lead soon after.
After serving his way to a 2-1 lead in the third set, Djokovic ramped up his efforts and was met head-on with Nishikori's increase in tempo, but the No. 24 seed missed three break points at 2-2 and was soon trailing.
However, the 31-year-old has looked back to something approaching his best at Wimbledon.
But Djokovic appears to be building towards somewhere near his best again and, while made to work hard by Nishikori, he was good value for a 6-3 3-6 6-2 6-2 triumph. It was not a surprising result, but a pleasing one.
A glimpse of the potential that has seen Khachanov's reputation grow came in the first game as a superb cross-court forehand helped him break.
With Kevin Anderson taking nearly three and a half hours to tame French showman Gael Monfils in the previous match, Djokovic knew he had about two hours of daylight left if he wanted to avoid coming back on Tuesday's rest day to finish off the contest.