Kenya’s Rudisha was all class in a smooth 800m victory which made him the first man since New Zealand’s Peter Snell in 1964 to win the event at consecutive Olympics.
“It is great to win such a big competition, my second gold,” Rudisha said. “It’s so great. I am so excited. It is the greatest moment of my career.”
But Rudisha was soon upstaged by the Bahamas’ Miller, who threw herself head-first across the line to snatch victory from flummoxed American favourite Allyson Felix.
More was to come when Braz stunned French defending champion and world record-holder Renaud Lavillenie to win the pole vault, grabbing Brazil’s second gold of the Games and bringing the sparse crowd to its feet.
Earlier, a wobble on the balance beam ended Simone Biles’ bid for a record five gymnastics gold medals, and Rio had its latest safety scare when a giant suspended TV camera plunged to the ground, slightly injuring seven.
Miller remained lying on the track for some time after her unconventional dive, which followed a similar lunge across the line by Brazil’s Joao Vitor de Oliveira to qualify from his 110m hurdles heats.
“I’ve never done it before. I have some cuts and bruises, a few burns. It hurts,” Miller said.
“When I was on the ground I didn’t know I’d won. I still don’t know how it happened. What was in my mind was I had to get a gold medal. The next thing I was on the ground. It’s an amazing feeling.”
Her last-ditch plunge meant disappointment for America’s Felix, who has Olympic gold medals over 200m, 4x100m and 4x400m but who switched to focus on the longer distance.
The desperate dives came on a treacherously wet night when runners clattered into hurdles and the discus slipped from hands before officials called a 20-minute suspension.
Conditions were so bad that an extra 110m hurdles heat was arranged for competitors who didn’t qualify from the first two races, when the rain was torrential.
As the rain eased, Kenyan middle-distance star Rudisha emerged to stamp his class on the 800m.
The world champion and world record-holder hit the front in the final 300m and had one more gear than his rivals as he swept to the line in 1min 42.15sec.
In the pole vault, Lavillenie was the hot favourite but he was undone by Braz’s Olympic record of 6.03m and had to settle for silver in front of the partisan crowd.
“In 1936 the crowd was against Jesse Owens. We’ve not see this since. We have to deal with it,” said the Frenchman in response to the jeers he received in a comparison sure to be judged as being in extremely poor taste.
Gymnast Biles was confident of claiming her fourth Rio win and move into position for an unprecedented fifth on the last day of the competition on Tuesday.
But the tiny Texan wobbled badly on the balance beam when landing a forward somersault and had to put both hands down for support.
It was a bewildering upset for Biles, 19, who hadn’t lost a final since 2013 but wound up with bronze as the Netherlands’ Sanne Wevers topped the podium.
“Everyone would love to have a bronze at an Olympics. I’m just disappointed with my routine. I don’t really know what happened,” said Biles.
At the velodrome, Elia Viviani recovered from a mid-race crash to beat celebrated British sprinter Mark Cavendish in the men’s omnium.
“I’m not angry, it’s a bike race,” said the 27-year-old Italian after the crash, which left South Korea’s Park Sang-Hoon in hospital with friction burns and bruises.
Gymnast Eleftherios Petrounias, who is 5ft 5ins (1.64m) and was bullied a child for his lack of height, stood tall for Greece when he won the rings event.
And North Korea’s Ri Se-Gwang had tears in his eyes and saluted military-style as he accepted his gold medal in the men’s vault.
Off-field hiccups have dogged the Rio Games but there could have been tragic consequences when a suspended TV camera the size of a small motorbike crashed at the Olympic Park precinct.
Seven people suffered minor injuries when two ropes securing the ‘spidercam’ snapped simultaneously and the camera plummeted 20 metres (65 feet).
Then, as the day closed, a bush fire threatened the mountain bike centre at Deodoro in the west of the city.
Also on Monday, Kenyan-born Ruth Jebet won Bahrain’s first ever Olympic gold when she claimed the women’s 3000m steeplechase, and Poland’s Anita Wlodarczyk broke her own world record en route to the women’s hammer title.