Holt's second-half strike, his 25th goal of the season, deepened the home side's relegation fears.
Oldham belied their lowly status and both Dale Stephens and Reuben Hazell went close to scoring in the opening 20 minutes.
Norwich then burst into life, with Holt squandering a good chance from Wes Hoolahan's cross and also heading inches wide from eight yards.
Holt found the finishing touch on 53 minutes when he stretched to score at the far post after smart wing play by Anthony McNamee.
Oldham substitute Keigan Parker should have levelled eight minutes from time after running clean through, but Fraser Forster saved well. And Norwich made sure of the points moments later as Korey Smith made a goalline clearance from Hazell.