The 20-year-old from Botswana was trailing heading into the final 50 metres, but he dug deep to find an extra burst to defeat Kenya's Rudisha in a time of one minute and 45.18 seconds.
Amos goes some way to avenging the 2012 London Olympic Games when he finished second to Rudisha " who produced a world-record time to take gold.
Speaking to BBC Sport after the race, Amos paid tribute to Rudisha: "I am so happy but David Rudisha will always be the hero of 800 metres."
There was a clean sweep of the medals for Jamaica in the men's 200m, Rasheed Dwyer topping the podium ahead of Warren Weir and Jason Livermore.
Dwyer came off the bend strongest and dipped for the line to record a time of 20.14secs.
Blessing Okagbare became a double Commonwealth champion as she added the 200m title to her 100m triumph.
The 25-year-old made an electric start and, although she faded somewhat towards the end, she had more than enough to win in a time of 22.25secs ahead of English duo Jodie Williams and Bianca Williams.
World champion Jehue Gordon was one of the star attractions in the men's 400m hurdles but the Trinidadian was defeated in a keen battle down the straight by South Africa's Cornel Fredericks, who overcame heavy strapping on his thigh to seal the gold.
Jeffery Gibson of the Bahamas collected a bronze medal, while Jamaica's Annsert Whyte fell to the ground in the final stages.
In the same event in the women's race, a false start ensured a nervy field but favourite Kaliese Spencer clocked a time of 54.10secs to win gold for Jamaica, while Scotland's Eilidh Child added a silver medal to the one she collected in Delhi four years ago.
India's Vikas Shive Gowda posted a distance of 63.64 metres to win the men's discus to atone for the disappointment of finishing second in Delhi, while Nigeria's Ese Brume jumped 6.56m to win the women's long jump.
Linda Villumsen and Alex Dowsett claimed time trial gold in the respective men's and women's events.
In gymnastics, England's Max Whitlock made it three gold medals for the Games by taking top spot in the men's floor.
Claudia Fragapane also made it a hat-trick of Commonwealth golds for England by winning the women's vault, and compatriot Rebecca Downie now has a pair of golds, the 22-year-old the victor in the uneven bars.
In weightlifting, Canada's George Kobaladze took first place in the men's +105 kilogramme Group A, while Canada's Tamerlan Tagziev and India's Yogeshwar Dutt were winners of the men's 86kg class and 65kg class respectively in men's wrestling.
There was more wrestling success for Canada in the women's 63kg class for Danielle Lappage, with Babita Kumari the gold medallist for India in the 55kg class.
Malaysia's Ooi Tze Liang was crowned champion in the men's 3m springboard diving final, as Canada's Meaghan Benfeito secured the same honour in the women's 10m platform.
England won the women's triples lawn bowls gold-medal match against Australia, with South Africa beating Wales to earn bronze.
The day's action was rounded off by the heats of the women's 100m hurdles, where Olympic and Commonwealth champion Sally Pearson signalled her intent with a time of 12.69secs.
Her performance comes after Athletics Australia's head coach was suspended following his decision to publicly criticise Pearson for not attending a pre-Games training camp.