In the dramatic final round, the eight-lap race was restarted twice after technical infringement by the riders and in the third start, Azizulhasni pipped world champion, Joachim Eilers from Germany to finish third.
The 28-year-old Melbourne-based rider crossed the finishing line for the bronze behind defending champion Jason Kenny from Britain and Dutchman Matthijs Buchli.
Azizulhasni, who was earmarked as gold medal prospects, won the Olympic medal in his third attempt after failing to qualify for the finals in the 2008 Beijing Games and sixth placing at the 2012 London Games.
"I dedicate this medal to all Malaysians and to my wife and kids who sacrifice alot over the years," the rider, who is known as 'Rocket Pocket Man' for his pint-size body.
"Although I was going for the gold, but the bronze is the result of hard work over the years and the beginning to mount for the gold in the 2020 Tokyo Games," said the rider who leaves Rio for home tomorrow night.
In the one day-race, Azizulhasni was one of the six cyclists and only Asian to qualify for the final from the repechage rounds.
In the repechage, he had former world champion Theo Bos of Holland, Canada's Hugo Barrette and Czech Republic's Pavel Kelemen in the first heat and won the top spot to qualify for the second round.
In the second round's first heat, Azizulhasni finished third behind Jason and Matthijs, while Joachim, Poland's Damian Zielnski and Colombian Fabian Hernando Puerta Zapata emerged top three in the second heat.
The top three in the two heats moved in to the final.
Azizulhasni is the first cyclist for Malaysia to win a medal in Olympics.
His bronze medal feat is the second medal for the country after diving pair, Pandelela Rinong and Cheong Jun Hoong contributed a silver in the synchronised 10m platform last Tuesday.
