He needed all of his famed final lap speed to come home in 13:26.98, ahead of Ethiopia's Hagos Gebrhiwet (13:27.26) and Kenyan Isiah Kiplangat Koech (13:27.26), six days after winning the 10,000 metres in Moscow.
Farah, defending his title from Daegu, became the only man apart from the peerless Kenenisa Bekele to hold the Olympic and world championship distance double simultaneously.
"I never thought in my career I would achieve something like this. This was very tough - it was all left to the last two laps. I had a lot of pressure but at the same time I enjoy it," he told BBC radio.
"This is something I work so hard for. I was thinking about my kids, how long I spend away from them. It's very difficult because they're growing so fast and I haven't been around for the last four or five months.
"It was hard this year, harder than last year."
In a final of muddling and erratic pace, the trio of Ethiopians and Kenyans did their best to disrupt the Briton with team tactics but Farah, towards the back early on, went to the front with three laps to go.
With his principal rivals for gold, all with fresher legs after not running in the 10,000, queuing up to pass at the bell, Farah gritted his teeth, pumped his arms faster and refused to yield.
Koech appeared the main danger around the final bend but did not have the legs to get past as Farah held him at bay all the way to the line and Gebrhiwet's late burst snatched silver by one thousandth of a second.
(Editing by Ed Osmond)
