The 6-2 7-6 (7/3) 6-4 scoreline does not remotely tell the story of a match where 2009 champion Del Potro threw everything at last year's winner only to see it come back with interest.
Djokovic said: "Even though it was straight sets it was much closer than that. He's a great player. I was lucky in the second set.
"We played some incredible points. It's always entertaining to play at night, so much fun. This is very special and I'm really happy to be in the semi-finals."
Djokovic will now play fourth seed David Ferrer, who beat Janko Tipsarevic in another classic earlier on Thursday, in a rematch of a last-four clash from 2007.
Djokovic lost to Roger Federer in the final that year but, with the world number one knocked out by Tomas Berdych on Thursday, the second seed assumed the favourite's mantle.
So easy had the Serbian's progress been until this point, it was difficult to tell how well he was playing.
Djokovic had seemed out of sorts at Wimbledon and the Olympics, where Del Potro beat him to the bronze medal, but he showed on Arthur Ashe Stadium he is back to the form that brought him three grand slam titles last season.
The second set was undoubtedly the best of the tournament as Del Potro found his rhythm on his huge groundstrokes but still could not break down Djokovic's legendary defences.
The second seed went an early break down but broke back when Del Potro served for the set and then created three set points in a titanic 12th game that lasted more than 17 minutes.
The Argentinian saved those but could not resist the sheer force of Djokovic in the tie-break, and a break at the start of the decider eventually proved the difference.
Djokovic has now reached 10 straight grand slam semi-finals, and Del Potro admitted the better man won.
He said: "I had to win that second set. Nole [Djokovic] played really well in the most important moments. In the tie-break he was a little lucky on some points. But he deserved it, he played much better than me for the rest of the match. He was too much for me.
"He's playing better and better every match, he's the favourite to win. He played at a very high level for the whole three hours and I wish him the best."
If Djokovic and Del Potro was the main event, Ferrer and Tipsarevic served up a brilliant appetiser with five sets of captivating tennis.
Ferrer, who is having the season of his life, was the clear favourite and won the first set reasonably easily but Tipsarevic dug in, steeled himself to trade with the most dogged competitor in tennis and almost won.
He clinched a second-set tie-break, letting out a huge roar, and then won five games in a row with spectacular attacking tennis to lead by two sets to one.
Ferrer was hanging on but the Spaniard never gives up on a point let alone a match and he found the breakthrough in the fourth to level up.
Tipsarevic turned the tables at the start of the decider to lead once more but a heavy fall at the end of the sixth game seemed to affect him and Ferrer hit back.
A tie-break was the only way to split them and it was the Spaniard who prevailed, dropping to the court and letting out a scream of delight as he came through 6-3 6-7 (5/7) 2-6 6-3 7-6 (7/4).
Speaking on court afterwards, Ferrer said: "I don't have words. I'm very happy. I ran a lot. It was a really tough match. Janko is an amazing player. He fought a lot and he deserved also to win today [Thursday]."
Tipsarevic also reached this stage last year, losing to Djokovic, and he came off the court feeling he could not have done anything else.
The eighth seed said: "I don't really feel that I screwed up in any way, that I played bad, I mis-hit, or I double faulted or anything like that. I'm just feeling really sad that I'm not on the other side of the net like a victor."
The fans on Arthur Ashe were so impressed by the efforts of the two men that they gave them a standing ovation before the deciding tie-break.
Tipsarevic added: "I would like to thank the crowd, which was amazing. It's not maybe a quarter-final which they wanted to see, without Rafa [Nadal] being there, but I think David and me played, until now at least, the best match of the tournament."