Anderson spurned the chance for another break when he rammed a forehand into the net and was forced to settle for a tiebreak after Federer recovered from 30-0 down in the final game of the set.
His opponent on Wednesday is eighth-seeded Kevin Anderson, the first South African since Wayne Ferreira in 1994 to get to the last eight.
Nadal has made the quarter-finals for the first time since finishing runner-up to Djokovic in 2011. I think people can see that and can feel that.
"It's a pretty exciting opportunity to play Federer here at Wimbledon", said Anderson, who has never beaten the 20-time Grand Slam champion in four attempts.
Djokovic copped a code violation for unsportsmanlike conduct after flinging his racquet into the grass behind the baseline in frustration early in the third set.
Deploying his huge serve to lethal effect, Anderson roared back to leave the champion's title bid in tatters thanks to a barrage of 28 aces and 65 winners. "I couldn't really get the rallies going the way I wanted to, especially the 1-2 punch wasn't working at all today".
"It was quite a odd feeling for me not to be able to deliver my game that I know I possess, that I know I've been delivering for so many years", Djokovic said ahead of Wednesday's quarter-finals.
The 20-time Grand Slam victor is aiming for a 13th Wimbledon semi-final and to extend his record for the most last four appearance at the All England Club in the Open Era, having taken sole ownership of the record from American Jimmy Connors during his 2017 title run. But I also have a feeling, it was a feeling of mine, you know, not getting it right.
Federer didn't seemed bothered by being away from Centre Court when he cruised through the first set in just 26 minutes.
Federer, 36, breezed through the opening set in just 26 minutes, had a match point in the third set and was just two points from victory a few times in the epic fifth set that lasted 90 minutes.
The eight-time champion and 20-time grand slam victor last played a Wimbledon match outside Centre Court in 2015.
Many are already anticipating a Sunday final between Federer and Nadal, 10 years after their 2008 epic championship showdown widely regarded as the greatest final ever played.
The gentleman player, who authored a spirited turn around on Court No.1 pulled off a 2-6, 6-7 (5-7), 7-5, 6-4, 13-11 win in 4 hours and 14 minutes.
Federer eventually stemmed the tide with a love hold, and the set was back on serve when Anderson failed to clear the tape with a forehand after saving two break points. "I've been playing well", Federer added.
As the fifth set became as much a test of mental strength as anything, from 4-all to 6-all to 8-all to 10-all, Anderson was as steady as he needed to be.
Federer fell to 266-3 in career Grand Slam matches where he won the first two sets.
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As scorching as Alli's play has been during this World Cup , Mae's career is equally on a skyrocketing, upwards trajectory. However, they are four places ahead of Sweden who England defeated 2-0 in the quarter-finals.
England have not been in the semi-finals of the World Cup since 1990 when they lost on penalties to then West Germany. How are the English feeling? We have come back after 20 years to the semis and we deserve it.
Mr Trump and his wife Melania arrived at Stansted airport, where he was met by the UK's global trade secretary Liam Fox. The dinner is Trump's official welcome to the United Kingdom during their first visit since Trump's election.
Djokovic overcame a series of rows with the chair umpire to record a 6-3 3-6 6-2 6-2 victory over Japan's former US Open finalist. Things got worse between the two later when Djokovic felt Ramos failed to sanction Nishikori for a similar act in the fourth set.
Meghan's dress is a bespoke Dior number and is a similar design to the wedding dress she wore to marry Prince Harry . Her hat, by Jane Taylor, was a headband-style piece with floral accents, and completed the elegant look.
In her response, Mrs May said that "I do not agree with your characterisation of the policy we agreed at cabinet on Friday". We are yet to have clarity around questions of design, quality and delivery methods concerning the homes we build.
The birth came just weeks after Cardi B confirmed in a statement that she and Offset , 26, had been secretly married in September. She told Beats 1: 'It's like everybody is coming down my neck like, "Why are you not leaving him?" I know I look good.
Abbas also stressed that new attempts to negotiate peace between Israel and the Palestinian Authority led by U.S. President Donald Trump will fail, saying that Palestinians "will not let the "Deal of the Century" work".
Attacking allies over trade and their willingness to pay their share of military costs has played well with his political base. He described the current situation as "disproportionate and not fair to the taxpayers of the United States".
BMC take team time trial stage but Froome makes gains
Froome was left 55 seconds behind in the overall standings with another week of nervy rolling stages before hitting the Alps. It will be van Avermaet's second stint in yellow after three days in the maillot jaune during the 2016 Tour de France.
Fans thank England for 'making nation dream'
He said the players were " absolutely gutted " but the fans' reaction in the stadium after the game showed what they had achieved. Back then, a powerful West Germany team edged England in a penalty shootout after a 1-1 draw, and lifted the trophy days later.
Wimbledon 2018 -- Angelique Kerber advances to final
Kerber did not dictate much, content to let 2017 French Open champion Ostapenko determine the outcome of almost every point. Williams took the wheel early when she broke Gorges' serve in the fifth game of the first set.
Federer stunned by Anderson in Wimbledon thriller
How much longer we will get to feast on the delights of Federer is unclear, how many more Grand Slam titles he can amass unsure. Roger Federer , meanwhile, comfortably defeated Adrian Mannarino in a 6-0, 7-5, 6-4 victory to reach the quarterfinal stage.
Pompeo presses Europe to get tough on Iran
Sources told Reuters last month that private refiners Nayara Energy and Reliance Industries Ltd plan to halt Iranian oil imports. Three others are headed for undisclosed ports on India's west coast from the US Gulf Coast.