The Serbian was at his brilliant best, producing 43 breathtaking winners and scrambling around the Arthur Ashe Stadium centre court like a golden retriever, fetching everything the towering Del Potro threw at him.
Djokovic eventually won 6-2 7-6 6-4 to go into the last four as the only man yet to drop a set in the tournament but the score line did not reflect the intensity of a match where he was pushed to the limit.
"Even though it was a straight-sets win it was much closer than the score indicated," Djokovic said in a courtside interview. "I'm just happy to get through."
Djokovic's next opponent is the Spanish baseliner David Ferrer, who won a four and a half hour slugfest with Djokovic's countryman Janko Tipsarevic.
With both players close to exhaustion after running each other to a standstill in the mid-afternoon sun, Ferrer clawed his way back from 4-1 down in the final set to win the deciding tiebreaker and triumph 6-3 6-7 2-6 6-3 7-6.
"It was an emotional match," said Ferrer, who has made four grand slam semis in his career but never a final.
'Deserved to win'
"My opponent, he deserved also to win this match. In one tiebreak it's a lottery and I was lucky in important moments."
Battered and bruised by the battle, Tipsarevic tumbled heavily to the court in the fifth set and twice called on his trainer to have his foot and thigh taped.
"I think it was a high intense match with not too many ups and downs," he said.
"Both of us are baseline players, both of us are big fighters on court, so something like this was only expected."
With the last grand slam of the season reaching its climax, the first trophies were handed out on Thursday when Russia's Ekaterina Makarova and Brazil's Bruno Soares won the mixed doubles final.
The pair, who literally teamed up at the last minute when Soares was told he would not qualify for the field with his original partner Jarmila Gajdosova, came from behind to defeat Czech Kveta Peschke and Marcin Matkowski of Poland 12-10 in a deciding tiebreaker after splitting the first two sets 6-7 6-1.
"At the very last minute, 11:59, I signed us in. I guess it worked out," said Soares.
Booking a place
Olympic champions Bob and Mike Bryan booked their place in Friday's doubles final against Leander Paes and Radek Stepanek while French Open champions Sara Errani and Roberta Vinci of Italy advanced to Sunday's women's final against Czech pair Andrea Hlavackova and Lucie Hradecka.
Errani is also due to play Serena Williams in the singles semifinals on Friday, with the winner to meet Victoria Azarenka or Maria Sharapova in Saturday's final.
The men's singles resume on Saturday, with Olympic champion Andy Murray squaring off against Czech Tomas Berdych in the other semifinal.
Despite losing his number one ranking to Roger Federer this year, Djokovic has been the most consistent player in the majors over the past two seasons, reaching the semifinals in the last 10 grand slams.
Only Federer, who made 23 consecutive semis during his peak, has made more but Djokovic is in exalted company, joining Rod Laver and Ivan Lendl in second place with 10.
The defining moment in his win over Del Potro came late in the second set, which went 84 minutes. The Argentine served for the set at 5-4 but Djokovic broke back and eventually won it in a tiebreaker after the 12th game lasted 17 minutes.
"He is a quality player," Djokovic said of his opponent. "I was lucky in the second set. We had some amazing rallies and he hit some great groundstrokes." – Reuters