On a very tricky course at the VeloPark, Strombergs, the first Olympic champion in BMX in Beijing, started brilliantly and led to the finish in a time of 37.576 seconds.
Sam Willoughby of Australia - who along with Phillips was excellent in qualifying - came second, with Carlos Mario Oquendo Zabala of Colombia taking bronze.
Phillips, who only recently recovered from a broken collarbone, had impressed in the heats, also started well but was back in fourth when he went down.
He was not seriously injured and was able to finish the race a few minutes later, with American Connor Fields, who also went down, coming seventh.
Dutchman Raymon van der Biezen, who had clocked the best time in the seeding run and had won his three quarter-final runs as well as the first of three semi-final dashes, settled for fourth.
France's Joris Daudet, who was among the favourites coming into the Games, crashed in the third run of the semi-finals and did not take part in the final run on the 450-metre track at the VeloPark.
Winner Strombergs admitted he cried when he first saw a BMX race as a small child.
"When I started BMX, I was crying to be honest. I was five years old when my father took me to the BMX track and when I saw all those big guys jumping those big doubles, I started crying," Strombergs said.
"I said 'No way dad'. But after another month I said to my dad, 'OK, I'll go again' and that's how I started."
In the women's race, Mariana Pajon won the Colombia's first gold of the Games as Britain’s Reade finished well out of the medals.
The 2011 world champion Pajon - considered an outsider after an indifferent season but superb in the heats - started brilliantly and led to the finish in a time of 37.706 seconds, with New Zealand's Sarah Walker second.
Laura Smulders of the Netherlands took bronze, with British hope Reade - who crashed while leading the Beijing final four years ago - back in sixth after a poor start saw her stranded for most of the race.
World champion Magalie Pottier of France, and former world champions Walker and Reade had been the favourites, with the Briton dominant during the test event on the London course earlier this year.
Pajon, who was Colombia's flag-bearer for the opening ceremony, said: "I can't believe it.
"It's like a dream come true. I've been trying to win this my whole life. I just wanted go out of the gate and win it. It's unbelievable.
"I have tried so hard for it and I just did it. I won the three motos (runs) and the final. I felt really strong, I had really good gates and that's it. I really had fun on it. I have to wake up tomorrow and realise what I have just won."