Wycombe made a bright start with Jon-Paul Pittman firing over on the turn from close range after eight minutes, but from then on it was all Norwich.
Wes Hoolahan was first to go close for the visitors with a 25-yard drive just clearing the crossbar midway through the first half before Simon Lappin rattled the woodwork with a left-footed free-kick from the edge of the penalty area.
Chris Martin was next to trouble Wycombe as his rasping 30-yard free-kick also hit the crossbar and Chairboys goalkeeper Scott Shearer then had to tip Russell Martin's dipping volley over.
Shearer was called into action again 10 minutes into the second half as he spectacularly turned Russell Martin's long-range strike behind before Matt Phillips hit the post for Wycombe.
But the Canaries got the goal they deserved 13 minutes from time as Hoolahan pulled the ball back for Smith, who slid home his third of the season.