The world number one had yet to drop a set at Flushing Meadows this year, having lost just 15 games en route to beating Ricardas Berankis and Benjamin Becker in rounds one and two.
Meanwhile, both of Sousa's wins had been epic five-set encounters.
The unseeded Portuguese, who was ranked 95th in the world, had overcome Grigor Dimitrov 3-6 6-3 6-4 5-7 6-2, before beating Jarkko Nieminen 1-6 6-3 3-6 6-3 6-4.
Sunday's match was the first meeting between Djokovic and Sousa.
Find out how the action unfolded with Sports Mole's blow-by-blow text updates below.
11.58pmGood evening. Rafael Nadal, David Ferrer, Andy Murray and Tomas Berdych are all safely through to round four, having dropped just one set in all of their respective third round wins combined. Djokovic, who is due on court shortly, will be looking to ensure that he becomes the final member of the top five to reach the last 32 stage in comfortable fashion.
0.01amThe Serb will first have to work out his opponent, having never previously faced the 24-year-old.
0.05amSousa is 6'1" tall and, if he serves well, he can be difficult to break. However, he is also a rather inconsistent performer, who often suffers due to his own impatience on court.
0.07amHe is right-handed, with a two-handed backhand, and his game is best suited to clay. However, as his recent wins over Dimitrov and Nieminen suggest, he is capable of mixing it on a hard court.
0.09amSousa is competing in the main draw at Flushing Meadows for the first time this year, having failed to progress beyond the qualifying rounds in 2011 and 2012. He has never made the first round at Wimbledon, however he reached round two at both the Australian Open and the French Open earlier this year.
0.11amRight then, the players have completed their warm-ups and the world number one will serve to get us underway.
Djokovic 1-0* SousaThe Sousa backhand is struggling early on and Novak is not in a charitable mood. 30-30.
Djokovic 1-0* SousaBREAK POINT DJOKOVIC: Sousa plays one of his best points at 30-30, driving a meaty cross-court forehand onto the corner of Djokovic's baseline. That shot would be enough against most players on the tour, but not Novak, who gets incredibly low and scoops a glorious passing shot just out of his opponent's reach.
Djokovic *2-0 SousaDJOKOVIC BREAKS: Sousa saves the first break point with stinging cross-court shot, but Novak, who appears very keen to get forward early on, pushes back immediately to force the early break.
Djokovic 3-0* SousaThe Serb holds to 30. He is pouncing upon any sign of weakness and frequently getting to the net, where he has been deadly so far, winning six points from six.
Djokovic *4-0 SousaDJOKOVIC BREAKS: Sousa is attempting to be as aggressive as possible. That decision is pleasing the fans, as it is contributing to some attractive tennis. However, it is pleasing Djokovic even more. The Serb is being played at his own game and this is allowing him to pick his opponent off with superb accuracy. He breaks to 40.
Djokovic 6-0 *0-0 SousaFIRST SET DJOKOVIC: The Serb is dictating the play and he converts his second set point to break to 40 with a blazing forehand winner. The opening set is over after just 28 minutes.
Djokovic 6-0 *0-0 SousaSousa calls an injury time out. The trainer is on and doing some work on his left knee. Let's not forget that, although the previous set was very short, it was the Portuguese's 11th of the week.
Djokovic 6-0 *0-0 SousaDjokovic hit 14 winners and seven unforced errors in set one, while Sousa produced four winners and six unforced errors.
Djokovic 6-0 1-0* SousaNovak holds to love. There is no suggestion that Sousa's knee is causing him any problems. Djokovic is just in sublime form.
Djokovic 6-0 1-0* SousaThe Portuguese finds a few big first serves and they bring about a couple of game points. 40-15.
Djokovic 6-0 1-0* SousaAs I said earlier, Djokovic is not in a charitable mood. He saves the first game point with a smash at the net and then saves the next with a terrific pass, punishing Sousa for coming forward. 40-40.
Djokovic 6-0 1-0* SousaBoth players squander game points and we go back to deuce, before Sousa wins a stunning 21-shot rally to bring up another.
Djokovic 6-0 *1-1 SousaSousa holds! Novak is finally worn down and he finds the net. The Portuguese celebrates like he has just won the match.
Djokovic 6-0 2-1* SousaA champion's response from Novak, who holds to love for the third time tonight. He has dropped just four points in five service games.
Djokovic 6-0 *3-1 SousaDJOKOVIC BREAKS: The game ends with a double fault from Sousa at 15-40, but the two previous points were won thanks to excellent tennis from the world number one, who executed an unstoppable deep forehand and then bamboozled his opponent with a perfectly-angled backhand slice.
Djokovic 6-0 4-1* SousaThe fans want their money's worth and are understandably siding with Sousa. Djokovic fires a return just long, causing the locals to whoop and cheer. 15-0.
Djokovic 6-0 *4-2 SousaSousa holds again! More whooping from the crowd as Djokovic pushes a poor backhand long to bring about game point at 40-30. The Serb then shows signs of frustration for the first time in the match, as he smashes an angry forehand return low into the net on the next point.
Djokovic 6-0 *4-2 SousaIt was almost as if the world number one didn't want that last point because he didn't fancy being taken to deuce.
Djokovic 6-0 5-2* SousaAll of a sudden, there are errors left right and centre! Novak fails to convert set point at 30-40 as he plunders a backhand well long. Another missed backhand hands Sousa game point, but the Portuguese chips into the net. 40-40.
Djokovic 6-0 6-2 *0-0 SousaSECOND SET DJOKOVIC: The Serb brings about another game point with his 13th second-set winner. He then seals the set by forcing a forehand error out of Sousa.
Djokovic 6-0 6-2 *0-0 SousaDjokovic has now hit 27 winners and made 13 unforced errors, while Sousa has produced 16 winners and 20 unforced errors.
Djokovic 6-0 6-2 *2-0 SousaTwo rare unforced errors from Djokovic's forehand put Sousa 30-0 ahead in game 16. However, a third double fault and a missed backhand from the Portuguese level the game, before two unforced errors hand Novak a sixth break of serve.
Djokovic 6-0 6-2 3-0* SousaDjokovic double faults to go 15-15 but then quickly regains his lead in the game with an ace, followed by a backhand winner. Both players then trade forehand misses as Novak holds to 30.
Djokovic 6-0 6-2 5-0* SousaThe Serb starts game 19 with an unforced error on his forehand. However, a forehand winner, a miss from his opponent, an ace and a backhand winner allow him to hold to 15. Sousa must now serve to avoid receiving a third-set bagel.
Djokovic 6-0 6-2 *5-1 SousaBREAK POINTS SOUSA: Better late than never! The Portuguese hits a sweet backhand winner down the line and, at 15-40, he has his first break points of the match.
Djokovic 6-0 6-2 5-2* SousaSOUSA BREAKS: Djokovic saves the first break point by attacking Sousa's forehand and forcing a miss from his opponent. However, the world number one surrenders the game, to 30, on the following point courtesy of a sloppy backhand drive.
Djokovic 6-0 6-2 6-2 SousaGAME SET AND MATCH DJOKOVIC: Fuelled by anger at being broken, Djokovic destroys the Sousa serve and breaks to love to seal a 6-0 6-2 6-2 victory in one hour and 40 minutes.
2amDjokovic, who is still yet to drop at set at Flushing Meadows this year, will now face either Tim Smyczek of the USA or Spain's Marcel Granollers in round four.
2.03amNovak hit 34 winners and hit 26 unforced errors, while Sousa produced 10 winners and 27 unforced errors.
2.06amDjokovic made three aces and double-faulted twice. He got 68 per cent of first serves in, winning 79 per cent (30 of 38) of those points. The Serb also won a healthy 67 per cent (12/18) of points behind his second serve.
2.10amMeanwhile, Sousa's second serve let him down. The Portuguese, who made two aces and double-faulted on three occasions, won just 26 per cent (10 of 38) of points behind his second serve. He won 30 of 54 (56 per cent) first-serve points and his first-serve percentage was 59.
2.12amBoth players averaged 109 mph with their first serves. Djokovic dropped his speed to 89 mph on his second, while Sousa fell to 87 mph.
2.14amNovak was very successful at the net, winning 73 per cent of points (22 of 30). Sousa also came forward frequently, but with less success. The Portuguese won 48 per cent (10 of 21) of points at the net.
2.16amThat is all from me for tonight. I will leave you with a link to Liam Power's match report. Good night.