Van Der Burgh, who was coming back from a knee injury, led at the turn but Sprenger powered through to touch in a time of 58.79 seconds, with the South African just behind in 58.97. Felipe Lima of Brazil took bronze with 59.65.
"I remember getting to that first wall and thinking, man I'm travelling really fast and it's not even hurting at all, so I knew I was on track," Sprenger said.
"I could see Cameron in the corner of my eye and I knew he had gone out fast, but I have a stronger back end so it was my turn to come back," added the 27-year-old, second behind Van Der Burgh in London.
"The first thing I saw was Cameron's block and it had the two lights showing and I thought, oh I think I've got him. And then I turned around and saw 58.7 and it blew my mind."
Hungary's Katinka Hosszu won the women's 200 metres individual medley as Olympic champion Ye Shiwen of China surprisingly finished outside the medals in fourth.
The 24-year-old Hosszu, sixth at the last edition in Shanghai two years ago and a bronze medallist in Rome in 2009, led on all four legs and touched in a time of two minutes and 07.92 seconds.
Alicia Coutts of Australia took silver in 2:09.39, repeating her second place from 2011, and Spain's Mireia Belmonte Garcia delighted the home support with bronze in 2:09.45.
Belmonte Garcia held off Ye on the final leg, with the Chinese failing to defend her world title and finishing fourth in 2:10.48.
Cesar Cielo of Brazil won a second consecutive men's 50 metres butterfly title.
Victory for Cielo, a gold medallist in Shanghai, made him only the second man to win the 50 metres butterfly twice after South African Roland Schoeman.
In a relatively slow race, Cielo touched in 23.01 seconds and was close to tears on the podium as his national anthem boomed out around the arena. American Eugene Godsoe took silver in 23.05 and Fred Bousquet of France was third in 23.11.
"It was a very tense final, everyone was very nervous," Cielo, 26, said.
"I think my finish was the key, I think I just put my hand on the wall and I would say that last 10, even the last five metres that was the main difference for me," he added.
"The final is not the time to swim fast, the final is the time to touch first and I'm not surprised we swam a little slower tonight."
Swedish teenager Sarah Sjostrom won the women's 100 metres butterfly.
Sjostrom, 19, champion in Rome in 2009, finished strongest to touch in a time of 56.53 seconds, while Australia's Alicia Coutts repeated her silver medal from the last championships in Shanghai two years ago with 56.97.
Olympic gold medallist and world record holder Dana Vollmer of the United States was third in 57.24.
Lithuania's teenage Olympic champion Ruta Meilutyte set a world record of one minute 04.35 seconds in the semi-finals of the women's 100 metres breaststroke.
The 16-year-old, who won gold at the London Olympics last year, broke the previous mark of 1:04.45 set by American Jessica Hardy in 2009.