The Canaries took the lead in the first minute after some poor defending by Oxford.
Norwich goalkeeper Dan Grimshaw sent a long ball over the top which Toure was able to sprint onto and slip past the onrushing Jamie Cumming before slotting into an empty net.
The Canaries made their dominant start count again on 19 minutes when Ben Chrisene broke into space down the left and curled a low ball into the box that found Toure who slammed it into the roof of the net from close range.
It was the striker’s second goal of the game and his third in two matches after signing for the Canaries at the start of February.
Oxford started the second half in brighter fashion and Myles Peart-Harris had a shot from just outside the box fly narrowly over the bar, but it was the visitors who again found the net just moments later.
Toure was played in down the right and looked assured as he powered the ball across the keeper and into the bottom left-hand corner of the net for his hat-trick.
The Oxford fans were on their feet calling for a penalty with just over ten minutes remaining as Jeon Jin-Woo was brought to the floor with his back to goal, but referee Sam Allison waved away their appeals.
