The 18-year-old came through on the inside with a matter of metres to go to claim the title and set a new Paralympic record.
The race had looked set to be a battle between Kenya's David Korir and Moroccan Abdelillah Mame, but as they ran out of energy at the end, Baka ran past to win in 1:53.01.
Korir took silver, 0.15 seconds adrift, with Mame taking bronze.
Baka said: 'My finish was exceptional. I was looking for that corridor from the 200m mark and I found an opening 10m from the end.
'I made the most of it; I took my chances. I could have been second or third but it went my way.'
Australia's Evan O'Hanlon won his second gold of the Games as he added the 200m title to his 100m crown.
The T38 sprinter ran a world record 21.82 to finish well clear of South African Dyan Buis, with China's Zhou Wenjun getting bronze.
O'Hanlon, who has now retained the two titles he won at Beijing 2008, said: 'I came in and I've won 100 per cent of my races in world record time, the same as I did in Beijing.
'In Beijing I had an extra race (the sprint relay, in which he also took gold), but here I was approaching it to get as far below the world records as possible, and I've beaten both of them so I'm really happy.'
There was a Shot Put world record too as Mexico's Angeles Ortiz Hernandez extended the F58 mark to 11.43m to take gold, but only just.
With F57 athletes also in the competition, that equated to 1015 points, a mere three points clear of Bulgaria's Stela Eneva. Nigeria's Eucharia Iyiazi won bronze.
It was double joy for Mexico this morning as Luis Alberto Zepeda Felix was crowned the Javelin - F54/55/56 champion.
Silver went to Russia's Alexey Kuznetsov and bronze to Manolis Stefanoudakis of Greece.
Tunisia's Neda Bahi took the 400m - T37 title ahead of silver medallist Viktoriya Kravchenko of Ukraine and Russia's Evgeniya Trushnikova.
Brazil's Shirlene Coelho threw a world record 37.86m (1015 points) to win the Javelin - F37/38, China's Jia Qianqian getting silver and Australian Georgia Beikoff bronze.
There was an Azerbaijani one-two in the Trimple Jump - F12 as Oleg Panyutin and Vladimir Zayets finished first and second.
China's Dong Hewei came away with bronze.