Djokovic looked a man on a mission when he took just 15 minutes to blast to a 5-0 lead over Anderson and was somewhat frustrated when his opponent eventually made him work for almost two hours for his victory.
Such is his heightened level of expectation in the wake of his recently-ended 43-match winning streak that Djokovic still did not look entirely happy, berating himself after a couple of late miscues.
"I may be hard on myself but I think every player is looking for perfection all the time and I'm really satisfied with my performances in the first two rounds," the Serb said.
"Mentally I do have a different approach to Wimbledon than I had years before. It's obvious because of the winning streak that my confidence is very high and it makes it easier to step on the court because you believe in yourself and you know that you can win against anybody."
Having started the match 17 minutes late, much to the frustration of the fans well aware of the forecast rain, Djokovic broke to love in the second game.
Striking the ball cleanly he looked in a different class to his 36th-ranked opponent but was briefly derailed when Anderson won the sixth game and received a sympathetic cheer from the fans.
As a South African who developed his game in the American Collegiate system, Anderson bridled at the idea of being branded a plucky loser and suddenly found his form.
His 6ft 7ins (2.03m) frame enabled him to get steep bounce in his returns and he fought back to 5-3 before Djokovic restored order to take the opening set.
After punching a double-fisted backhand to settle the game, Djokovic turned to pump his fists at his support team.
The four burly men - fitness, conditioning and nutrition experts and a coach - were all dressed in matching white outfits and sunglasses and rose as one throughout the set to acclaim their man's key shots.
Anderson stayed in the second set to 3-3, when Djokovic found another gear to break to love again and the Serb was untroubled from then on.
"Efficiency is the right word in these conditions," he said. "Precision rather than speed in this wind. At the important moments I served well and returned well."
Djokovic's remarkable winning streak came to an end at the hands of Roger Federer in the French Open semi-finals and if the seedings go to plan they will meet at the same stage in this tournament.
Robin Soderling fought back from two sets down to beat Australian Lleyton Hewitt 6-7 3-6 7-5 6-4 6-4 in a dramatic second-round match under the Centre Court roof.
The Swedish fifth seed looked to be on his way out of the tournament as a succession of unforced errors gifted the former champion a two-set lead.
"I knew if I could raise my game after the first two sets I had a good chance," Soderling said.
"Of course it's tough. I never came back from two sets to love down before in my career. I think I was a little bit unlucky to not win the first set.
"You just have to start over, like trying to take one point at a time and see it as a new match, there's still a chance to win."
Hewitt did not even need to show his trademark feisty qualities, keeping the ball in play and waiting for Soderling to put it in the net or out of court.
The Swede, twice French Open runner-up, found no answer to his problems and Hewitt looked certain to wrap up a straight-sets victory until Soderling conjured a break out of the blue to take the third.
Suddenly Soderling found the range on his booming serve and as the 30-year-old Hewitt began to tire he started making more unforced errors.
Soderling again managed to break his opponent's serve to take the set and the match headed into a decider.
Hewitt, cheered on by his loyal green-and-gold clad fans, tried to pump himself up and aided by a few cries of "C'mon" he broke Soderling's serve to lead 2-1.
But the Swede broke straight back and Hewitt soon found himself serving at 4-5 to stay in the match.
Soderling upped his game and a brilliant crosscourt forehand helped set up three match points, the first of which he converted when Hewitt lamely netted a forehand.
The victor sunk to his knees and punched his chest before the players left the court to a standing ovation.
"I knew if I could raise my game after the first two sets I had a good chance," Soderling said. "It was nice to see him (Hewitt) injury-free and it was the best match we have ever played. He is a great fighter and he is playing better than for a while."
Del Potro, who was furious when the clash was suspended on Wednesday by bad light just after he had dropped the first set, stormed through the next two sets after the resumption before also sealing a more competitive fourth set to book a clash with Frenchman Gilles Simon in the third round.