The match was halted as dusk closed in after world number one and defending champion Djokovic had fought back from two sets down having been thoroughly outplayed by a fired up Anderson before rediscovering his A-game.
It was a remarkable conclusion to a day when a whiff of predictability had permeated the hectic schedule in men's and women's draws.
Serena had earlier ousted big sister Venus in the battle of the Williams siblings, while Roger Federer, Andy Murray and Stan Wawrinka had claimed comfortable victories.
In fact, the action elsewhere was remarkably tame in comparison to the ebb and flow of the drama on Court One.
Few had predicted Anderson would be able to mix it with Djokovic, except maybe the Serb himself who said the statuesque 2.03 metre South African was in the form of his life heading into the match.
He was not wrong. Within a short time he was two sets down as Anderson served superbly and happily went toe-to-toe with Djokovic from the back of the court, a tactic with which few succeed.
The first two sets ended with Anderson edging nervy tiebreaks, before Djokovic revved into gear storming through the third 6-1 and clinching the fourth 6-4 to leave the match in the balance and the crowd wanting more.
Sadly for them, the officials disagreed and boos rang around the arena as play was suspended until Tuesday.
The closeness of the encounter was in contrast to much of what had gone before.
The clash between the Williams sisters, who have won 10 Wimbledon singles titles, should have been the day's box-office smash, but drama was in short supply and the ending all too predictable.
BEST FRIEND
As has often been the case in the 25 matches between the siblings, the pre-game hype massively outdid the action on court, with Serena rattling through the opening eight points, and maintaining a stranglehold to wrap up the contest in 68 minutes.
She is now unbeaten in grand slams in 25 matches and edging closer to holding all four majors at the same time for the second time in her career -- although given the sensitivity of the occasion, any excitement was kept under wraps.
"It's hard to feel excited about (beating) someone you root for all the time no matter what and you love so much and is your best friend in the world," said Serena, whose next step en route to a 21st grand slam title will be against Victoria Azarenka in the quarter-finals.
Federer was given the swiftest of workouts against 20th-seeded Spaniard Roberto Bautista Agut, who became the latest player to exit in double quick time at the hands of the seven-time champion without making an impact on the Swiss's serve.
At one stage it looked like the Spaniard would struggle to finish the match as the trainer was called onto court to tend to an ankle injury, but he battled on in a 6-2 6-2 6-3 defeat.
The result extended a remarkable run of serving by Federer, who has not been broken in eight straight matches and 106 games, and set up a quarter-final with French 12th seed Gilles Simon, who surprised former finalist Tomas Berdych 6-3 6-3 6-2.
Murray's bid for a second Wimbledon title continued largely untroubled, with the third seed emerging unscathed from the crosshairs of Ivo Karlovic.
The giant Croat fired down 29 aces and regularly tipped the speed gun over 130mph but Murray made the most of his chances and, bar a brief wobble when he lost the third set, claimed a comfortable 7-6(7) 6-4 5-7 6-4 victory.
There was no upset in sight as the fourth seeds in the men's and women's draw went through in straight sets as Wawrinka edged Belgium's David Goffin 7-6(3) 7-6(7) 6-4 and Maria Sharapova beat plucky Kazakh Zarina Diyas 6-4 6-4.
The remaining days of the tournament are also likely to be quieter and less controversial after Australian hot-head Nick Kyrgios was beaten in four sets by Richard Gasquet.
(Reporting by Toby Davis; Editing by Ken Ferris)
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