Amos surged down the home straight to win while Rudisha, who tried to attack from the back, did not have the legs to catch him and finished third after being caught by Djibouti's Ayanleh Souleiman.
"I ran my own race, I felt very good," said Amos, silver medallist behind Rudisha at the Olympic Games, after winning in 1:43.77.
"It is no surprise for me to win the race today... I do not think about who is in the race, whether it is Rudisha or somebody else."
Rudisha, the world record holder, said he was glad to be nearly fully fit after an injury-hit season.
"I am at 85 or 90 per cent of my shape," said the Kenyan. "I am not at my best form.
"I wanted to see if I could run a tactical race from behind. I am happy now after my injury problems... Hopefully, I can come back strong next year, it was a good experiment for me, it was good to test myself."
World champion Lashawn Merritt managed to summon enough enthusiasm to win the men's 400 metres, cruising home in 44.36 seconds, more than 1/2 a second ahead of fellow American Gil Roberts with Botswana's Isaac Makwala in third.
"I was not that motivated for this race because I had been home for more than a month... and I had not raced for five weeks," he said.
"But this is my job, I did it for the people waiting for me. So, I motivated myself to come out and give a great performance."
Olympic champion Christian Taylor snatched the men's triple jump with his final leap of 17.51 metres, overhauling European champion Benjamin Compaore of France who had led with his second jump of 17.45
Jamaica's Kemar Bailey-Cole won the men's 100 metres ahead of American Michael Rogers and Britain's James Dasaolu, while Panama's Alonso Edward held off Jamaica's Nickel Ashmeade to win the men's 200.
South Africa's Commonwealth champion Cornel Fredericks pipped his rivals in the last few metres to win the men's 400 metres hurdles ahead of American Michael Tinsley and Puerto Rico's Javier Culson in 48.25 seconds.
"Next year, I would like to run under 48 seconds, this is my ultimate goal. And I would like to win an Olympic gold medal," said Fredericks. "I learn a lot with every race."
American Reese Hoffa was too strong for European and world champion David Storl as he won the men's shot put with a throw of 21.88 metres.
Croatia's Olympic, world and European champion Sandra Perkovic, who threw 71.08 metres to claim the European title at the same venue earlier this month, won the women's discus event with 68.36 metres, ahead of American Gia Lewis-Smallwood, the only woman to beat her this year.
But Perkovic was still not happy, saying:. "I am not satisfied with my winning result. I would like to have thrown over 70 metres, even 71 metres... I really came here to show more and it did not work."
There was a dramatic finish in the women's 1,500 metres when American pair Jennifer Simpson and Shannon Rowbury fell over the line after colliding in the last few metres.
Simpson just managed to hold on for the win after Rowbury made a dramatic late charge down the inside.
"That was a more dramatic finish than normal," said Simpson.
Jamaica's former 200 metres Olympic champion Veronica Campbell-Brown snatched the women's 100 metres in a photo finish from Ivorian Murielle Ahoure as both finished in 11.04 seconds with Nigeria's Blessing Okagbare just behind.
Dafne Schippers, who won the 100 and 200 at this month's European championships, was fourth.
American Dawn Harper-Nelson, the fastest in the world in the 100 metres hurdles this year, won the women's event in 12.58 seconds, ahead of Australia's Olympic champion Sally Pearson and Britain's European title holder Tiffany Porter who was third.
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