The 20-year-old, who is making his worlds debut, swam 58.52 seconds with Olympic champion Cameron van der Burgh of South Africa taking silver at 0.07secs as he lost out to Commonwealth champion Peaty on the wall.
Britain's Ross Murdoch took bronze at 0.57secs back.
This is the first time Britain has a world champion in the event since David Wilkie won both the 100 and 200m breaststroke titles at the 1975 championships in Cali, Colombia.
Peaty added the world crown to his Commonwealth Games victory in Glasgow last year, when he also beat Van der Burgh, and the pair are poised to resume their battle for the Olympic crown in Rio de Janeiro next year.
Peaty and Van der Burgh had broken the championship record three times between them in the heats and semi-finals in Kazan en route to the final.