Robles equalled the third-fastest 60 metres hurdles of all-time with his run of 7.34 seconds for a photo-finish win over Terrence Trammell, who was two-hundredths of a second behind to tie the American record.
“The world indoor record (Briton Colin Jackson’s 7.30 in 1994) will fall one day,” said Robles, whose best time is 7.33 seconds.
“I am as excited as breaking the world (outdoor) record,” the Olympic 110 metres hurdles champion added.
American David Oliver took third and Chinese defending champion Liu Xiang, who continues to recover from Achilles surgery, was seventh.
SECOND FAILURE
Isinbayeva left the championships perplexed after unexpectedly crashing out of a second consecutive global championship without a medal.
“I really do not know what happened,” said the 2008 Olympic champion and world record holder, who failed three times at 4.75 metres after opening successfully at 4.60.
“Maybe I was too tired emotionally,” said Isinbayeva. “I hope in the summer world records will come (again).
Brazilian Fabiana Murer claimed the gold at 4.80 metres, a mark Russian silver medallist Svetlana Feofanova also cleared.
Isinbayeva was fourth behind Polish outdoor world champion Anna Rogowska.
Tamgho, just 20, provided the shock of the three-day meeting with his world record leap of 17.90 metres on his final triple jump.
“I knew I had it in me because last year in Bercy I had a foul close to 18 metres,” the former world junior champion said.
“Today, I thought if I won, it would be around 17.60 metres. But after the Cuban (Yoandri Betanzos) jumped 17.69, I had to react.”
Betanzos finished second and compatriot David Girat was third.
Kenyan-born American Bernard Lagat also set a mark of distinction, winning his second 3,000 metres title six years after the first.
His time of seven minutes 37.97 seconds made him the oldest man to win a world indoor championships gold medal.
“My kids woke up at 7 a.m in the morning to watch their daddy,” Lagat said. “So I needed to show them something.”