Fachie and pilot Storey clocked a world record of 1:01.351 at the Velodrome.
Spain's Jose Enrique Porto andJose Antonio Villanueva took silver in 1:02.707, with Rinne Oost and Patrick Bos of the Netherlands coming third.
Afterwards, Fachie paid tribute to the support of the crowd. He said: 'The atmosphere was electric. The crowd pushed us round that final bend.
'I just can't believe it. To be here winning the gold medal is a dream come true.'
The crowd were great on that last lap. I thought I was dying at that point and it was a big push behind me.
Barney Storey
Storey echoed Fachie's appreciation of the Host Nation backing.
He said: 'The crowd were great on that last lap. I thought I was dying at that point and it was a big push behind me so that was great.'
Carol-Eduard Novak of Romania set a men's Individual C4 Pursuit world record of 4:40.315 to set up a gold medal ride-off with Czech Republic's Jiri Jezek (4:41.593).
Great Britain's Jody Cundy (4:42.005) and Diego Duenas (4:50.016) reached the battle for bronze.
The equivalent C5 event saw Australia's Michael Gallagher and Great Britain's Jon-Allan Butterworth reach the final after each clocking world records.
Butterworth recorded 4:35.026 before Gallagher beat the mark, clocking 4:30.012.
China's Liu Xinyang (4:35.386) and Yegor Dementyev of Ukraine (4:43.881) reached the bronze ride-off.
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