Nikica Jelavic put Everton ahead with a clever backheel before Jonny Howson equalised just prior to half-time with his first Norwich goal.
Jelavic added his fourth goal in four games to make it 2-1 in controversial circumstances after Norwich thought they should have had a foul, but the home crowd breathed a sigh of relief as Holt calmly swept home his 13th Premier League goal of the season with 14 minutes to go.
The sides cancelled each other out, employing similar tactics. Both played with intensity and constantly sought to close the ball down, meaning time and space - and therefore sustained periods of possession - were very rare.
Everton's opener came when Phil Jagielka's low cross was met by a neat turn and finish from Jelavic. The greatest criticism of Norwich would have been that the former Rangers striker Jelavic had too much space with which to score.
Norwich's pressing, however, eventually forced a goalscoring chance and the home side's equaliser. Adam Drury and the classy Wes Hoolahan combined well on the left wing before Hoolahan crossed superbly to assist Johnny Howson for the easiest of finishes. Hoolahan's cross had evaded the goalkeeper Tim Howard and Everton's defence before Howson tapped in into what was effectively an open goal to equalise.
It was difficult to see the pattern of play changing for the second half and so it was as the two sides continued to frustrate each other. Jelavic again gave Everton the lead but this time it was in rather controversial fashion; Norwich had appealed for obstruction by the midfielder Steven Pienaar when Everton were allowed to play on before Pienaar crossed low for another simple finish inside the area for Jelavic.
Norwich, however, continued as before and maintained the same pressure in an attempt to force the equaliser which eventually came in the 77th minute with Grant Holt's 15th goal of the season. It was a goal the striker deserved after a hard-working shift up front; when Aaron Wilbraham's shot was parried by Tim Howard, Aaron Wilbraham gathered the loose ball and squared for a simple tap-in Holt.
Thereafter, both sides played for the win yet though possession was very much end-to-end, it was without any creative quality and a suitable chance simply was not created. On balance, a draw was a fair result.