The Cottagers led 2-0 through Moussa Dembele and Muamer Tankovic but an own goal by Stephen Arthurworrey soon reduced the arrears and the late equaliser came after Fletcher was withdrawn in the 67th minute.
There were no chances of note during a quiet opening when the visitors showed exactly why they are unbeaten this season. Both teams played some neat football but it took almost half an hour for Reece James to attempt a shot that deflected behind for a corner following a lay-off by Will Keane.
From the set-piece, taken by James, Michael Keane headed back for his central defensive partner Tom Thorpe to loop a header onto the top of the net. Fulham came even closer to scoring when Buomesca Tue Na Bangna lifted a shot over Sam Johnstone that actually clipped the bar following some smart work down the right by the impressive Josh Pashley.
It proved to be only a reprieve for the Reds as, moments later, Lasse Vigen Christensen picked up a stray ball in midfield and combined with Dembele to allow the highly-rated forward to rifle past fit-again Johnstone with his left foot.
Kit Symons' side were good value for the lead at the start of the second half with Tom Richards blasting over and it was no surprise when, after a spell of pressure involved a number of corners, Tankovic was on hand to pounce from close range when one of them was headed towards him.
The champions really had to show their mettle and responded within a few minutes with Tyler Blackett speeding down the left and feeding Will