Another half-chance arrived for Fulham after seven minutes when Pajtim Kasami whipped a low cross into the Everton box, but there were no takers from the Cottagers.
Fulham continued to threaten and forced another opportunity after 14 minutes when Kasami met a flicked header from Brede Hangeland, but somehow the midfielder fired his effort wide from close range.
Kieran Richardson had the best chance of the half after 22 minutes following smart work from Moussa Dembele, but Tim Howard made the save. Moments later, David Stockdale denied Gerard Deulofeu in similar circumstances down the other end.
Howard was again called into action 15 minutes before the break when Holtby produced a powerful header inside the box, but the American shot-stopper made the stop during an end-to-end period of the match.
Ross Barkley tested Stockdale from outside the box in the latter stages of the first period, but once more the goalkeeper came out on top.
Dembele had a close-range header on the stroke of the interval for Fulham, but Howard made the save.