The exciting talent did not disappoint, taking a pass from Hazard just before the break and playing an immediate ball to Costa.
The Spain international looked marginally offside, but he finished with a clever dink with his right foot over the advancing Ruddy.
Traore, though, did earlier fluff a golden opportunity to claim his first Premier League goal. The revitalised Hazard sent him clean through in the 38th minute.
But the youngster, in his excitement, mis-controlled and Ruddy was able to collect.
Striker Cameron Jerome should have pulled a goal back in the 53rd minute, but unmarked eight yards out he lofted a half-volley well over the bar after being teed up by Russell Martin.
Nathan Redmond, though, lifted hopes in the 68th minute when he smashed past Thibaut Courtois after a smart pass by Wes Hoolahan to him in the box.
But it was not to be and with Sunderland drawing at home to Crystal Palace, the Canaries are now third from bottom.
NORWICH (3-4-2-1): Ruddy; Bennett (Mbokani 60), Martin, Klose; Pinto, Tettey (O’Neil 36), Howson, Brady; Hoolahan, Redmond; Jerome.
Subs: Rudd, Jarvis, Dorrans, Mulumbu, Olsson.
CHELSEA (4-2-3-1): Courtois; Azpilicueta, Cahill, Ivanovic, Kenedy (Rahman 69); Fabregas, Matic; Traore (Willian 60), Oscar (Mikel 60), Hazard; Costa. Subs: Begovic, Pato, Remy, Loftus-Cheek.
REFEREE: Lee Mason.