Sargent later missed a penalty for the Canaries, with his 56th minute attempt hitting the post from the spot.
Despite the miss, though, the Canaries added two more to their tally late in the second half to secure the victory, walking away with the clean sheet.
The 24-year-old's first half goal made it three-straight matches for the Canaries with a goal-contribution, and seven total in Sargent's nine appearances for Norwich this season.