Murray added the Rio title to his 2012 triumph and to his Grand Slam collection of the 2012 US Open and 2013 and 2016 Wimbledon crowns.
It also stretched the 29-year-old's current winning streak to a career best 18.
The final will go down as one of the best in the Olympics, lasting over four hours and ending with both men embracing at the net.
Del Potro, a bronze medallist in London four years ago, was inconsolable, weeping as he sat courtside.
"I had a lot of difficult losses over the last couple of years. I lost quite a few Grand Slam finals. I managed to obviously win a couple of big events and that meant a lot to me."
Murray also hailed 2009 US Open champion del Potro who has fought his way back from three wrist surgeries which threatened his career.
"What he's had to go through over the last three years or so with his wrists -- I can't imagine how mentally difficult that would have been," said the Briton.
The final was decided in a dramatic fourth set where del Potro was ahead twice with breaks to go 2-1 and 4-3 ahead.
But each time he faltered and Murray pounced. The Briton saved two break points for a 6-5 lead.
In a thrilling conclusion, two Argentine fans were even escorted out of the arena before Murray took victory on a second match point when del Potro netted a backhand.
Venus Williams, Martina Hingis and Rafael Nadal all suffered letdowns as the tennis tournament ended.
They lost 6-7 (3/7), 6-1, 10-7 to US compatriots Bethanie Mattek-Sands and Jack Sock.
Venus won singles gold at Sydney in 2000 and doubles titles with sister Serena in 2000, 2008 and 2012.
Despite the loss, she is still only the second player to have won five tennis medals after already being guaranteed silver by making the final.
The silver medal made up for a disappointing Games for the Williams sisters.
Defending singles champion Serena was defeated in the third round.
Hingis, 35, and playing her first Olympics since her debut in Atlanta in 1996, saw her gold medal hopes shattered in the women's doubles final.
She and Swiss partner Timea Bacsinszky lost to Ekaterina Makarova and Elena Vesnina 6-4, 6-4.
"If you asked me 10 years ago if I would be here in Rio, I would say you're crazy," said Hingis.
Kei Nishikori won Japan's first Olympic tennis medal in almost a century when he captured bronze against Nadal, despite the weary Spaniard mounting a stirring mid-match fightback.
Nadal, the 2008 singles champion in Beijing, was playing his 11th match in Rio.
But the 30-year-old did not go down meekly, fighting back from 2-5 down in the second set to push the play-off into a decider.
Nadal won the doubles gold with Marc Lopez on Friday and then lost an epic three-hour singles semi-final to del Potro on Saturday.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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