"I played only once in first four matches on Centre Court".
However, Federer was unable to break his own record after dropping the third set as Anderson embarked on a courageous fightback.
While Anderson is known for his booming serve, it's Federer's serve that has proved impenetrable at this year's Championships - the Swiss is yet to drop serve and has held in his past 81 service games, dating back to the first set of his semi-final against Czech Tomas Berdych last year. The 16-time Grand Slam champion also won their most recent meeting - French Open semi-final 6-4, 6-1, 6-2.
Since he exited Wimbledon at the first-round stage previous year, Anderson has enjoyed a solid return, making four finals, including his deep run at the US Open where he finished runner-up to Rafael Nadal.
The last time he won as many consecutive sets was in 2005 and 2006 at the height of his dominance. I think that was the key at the end.
The eighth-seeded Anderson trailed two sets to none and faced match point in the third set before staving off elimination to win the set 7-5.
Djokovic looked in control in the first set.
Police have spoken to Novichok poisoning victim Charlie Rowley
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Anderson scented blood and, out-duelling Federer time and again, he broke in the seventh game to level the match at two sets all.
After a slump following two years of nearly total domination of the men's game, Djokovic's star appears to be back on the rise and he is a clear contender to win a fourth Wimbledon title.
Nadal reached the quarterfinals of Wimbledon for the first time since 2011 after defeating Jiri Vesely in a 6-3, 6-3, 7-5 victory on Monday.
Anderson will take on the victor of the quarter-final clash between former Wimbledon finalist Milos Raonic and ninth-ranked John Isner.
Eight-time champion Federer has already won more Wimbledon singles titles than any other man, but was aiming to equal Martina Navratilova's all-time record.
On winning the match Anderson said: "I'm not quite sure what to say, I had to try my best to keep fighting". You can't plan for them anyway because one point can change the outcome of a set.
But after failing to convert a match point in the third set, Federer allowed a rash of errors to creep into his game, particularly on the forehand side. If it gnawed at him, there was no evidence as the match surpassed the four-hour mark.
That didn't seem to affect his focus, though, and neither did a time violation he was given when serving at 4-2, 30-30 in the fourth set.