Chances were few and far between during the opening 45 minutes, although Everton created the best opportunity in the early exchanges as Norwich goalkeeper Mark Bunn was called into action to deny Nikica Jelavic from close range.
The visiting Merseysiders always looked the more likely to break the deadlock before the break and they managed to do so with six minutes of the half left. A curling cross from Leighton Baines picked out Leon Osman, who guided a header beyond the reach of Bunn.
© PA Photos
The introduction of Kei Kamara shortly after the restart provided Norwich with a greater attacking threat and the Sierra Leone international had a chance to level up proceedings shortly after coming on. However, he was unable to keep his headed effort from close range on target.
He continued to be Norwich's major goalscoring threat though, and with nine minutes left he claimed the equaliser. The striker got above the Everton defence and managed to nod the ball beyond Tim Howard from inside the six-yard box.
It looked as though the spoils were going to be shared following Kamara's goal until Holt found himself free inside the area and he managed to beat Howard from close range.
Holt's intervention means that Norwich have won for the first time in 10 outings.