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Fulham had to wait 20 minutes before they had their first sight of the Cardiff goal, with Matt Smith attempting to head in at the near post after Ross McCormack won a corner, but he could not keep his finish on target.
McCormack was involved against just before the break as Fulham finished the first half strongly, but he rifled the ball just wide against his old club to leave the sides level at the break.
The visitors broke the deadlock just a couple of minutes after the restart though as Ben Pringle tried his luck from the sideline with a 40-yard effort, which was fumbled by Simon Moore to leave Smith to tap the rebound in.
Pilkington had the ball in the back of the net down the other end three minutes later as Cardiff tried to get back on level terms, but his header was ruled out for offside.
Fulham responded again though as they attempted to consolidate their lead, with Dan Burn charging towards the home side's box before setting up McCormack, who saw his effort blocked just short of the line.
However, the home side managed to get back on level terms with just three minutes still to play as Noone cut in from the wing before curling a left-footed strike into the top corner, securing a point for Cardiff.
The visitors pushed for a late winner as Moussa Dembele tried to pick out McCormack with a through ball, but Connolly was there to make another stop, ensuring that the sides finished level.