Marco Silva's side went behind to a goal from former Tottenham Hotspur youngster Jack Clarke just six minutes in, but Tom Cairney levelled in the 61st minute, and Fulham were handed a major reprieve right at the death when 15-year-old Chris Rigg's winner was ruled out for offside.
Fulham were one of two Premier League teams in action at 3pm, and Southampton hardly covered themselves in glory against second-tier opposition in Blackpool, but Nathan Jones's men still came away with a 2-1 win.
Left-back Romain Perraud scored twice either side of the half-time whistle for the Saints, whose sloppiness at the back allowed Arsenal loanee Charlie Patino to make things interesting in the 67th minute
Blackpool could not find an equaliser as Mick McCarthy's first game in charge ended in disappointment, but there was a late leveller at Ewood Park, as Birmingham City rescued a 2-2 draw away to Blackburn Rovers.
Reda Khadra put the visitors a goal to the good within just three minutes before Bradley Dack and Joe Rankin-Costello turned the game on its head, but substitute Jordan James - who had only been on the pitch for a couple of minutes - forced a replay with a stoppage-time equaliser.
Ipswich Town and Burnley also shared the spoils at Portman Road - albeit in a much more lowkey goalless draw - but the League One promotion hopefuls came agonisingly close to a late winner.
A cross-cum-shot from Conor Chaplin found its way over the head of Bailey Peacock-Farrell before coming back off the woodwork, as the Tractor Boys prepare for a second showdown at Turf Moor.
Yet another stalemate was played out at Hillsborough, where Sheffield Wednesday and fellow League One side Fleetwood Town shook hands on a 1-1 draw after more than 100 minutes of action.
The visitors drew first blood through Promise Omochere, but Josh Earl's own goal in the 71st minute rescued the Owls, who largely failed to make their dominant periods of possession pay.
Another encounter with more than 10 minutes of second-half injury time occurred at Kenilworth Road, as Luton Town were forced to settle for a 2-2 draw against League Two side Grimsby Town.
Gavan Holohan struck first for Grimsby before Elijah Adebayo's penalty and Jordan Clark gave Luton a 2-1 lead, but the Hatters were pegged back again by Harry Clifton.
Draws were certainly the theme of the afternoon, but despite the seven places between them in the Championship table, Bristol City passed the challenge of West Bromwich Albion with ease, recording a 3-0 victory at Ashton Gate.
Sam Bell and the highly-rated Alex Scott - aged just 20 and 19 respectively - had the ball in the back of the net before the half-time whistle blew, and the former made it a brace for himself early in the second half to cap off a dominant victory.