Norwich earned three points for new boss David Wagner in his first Championship game in charge as an assured first-half display paved the way for victory at Preston.
The injury-hit Lillywhites were swept away as a goal by Teemu Pukki and two from Kieran Dowell put the Canaries three up inside half an hour.
Tom Cannon, making his debut after arriving on loan from Everton, almost pulled one back after the break when Tim Krul tipped his shot on to the crossbar.
Any hopes of a comeback were snuffed out when Pukki slotted home his 11th of the season at the end of a slick move as Preston suffered their fourth consecutive league defeat.