Aleksandar Mitrovic fired the visitors in front after 14 minutes, reacting quicker than City defenders to a cleverly-angled ball towards the six-yard box from Cyrus Christie and planting a shot past Frank Fielding from close range.
But Lee Johnson’s men levelled after 35 minutes as Reid played a neat one-two with Josh Brownhill inside the area, creating space to beat Marcus Bettinelli with a left-footed finish from a narrow angle.
Two of the Championship’s most skillful sides went toe to toe from the start, both prepared to play out from the back and create openings with quick, accurate passing.
A pulsating first half saw Mitrovic force the first save of the game from Fielding with a fifth minute strike from the edge of the area.
But the on-loan Newcastle striker got the better of the keeper soon after to claim his first Fulham goal.
The strike provoked an immediate response from the hosts, with Hordur Magnusson heading just wide from a Jamie Paterson free-kick. The Icelandic defender will probably feel he should have scored.
Magnusson’s long throws caused havoc in the Fulham area at times, but the Londoners protected Bettinelli with some committed defending.
They were undone, though, by neat interplay between Brownhill and Reid, whose finish was unerring.
After the equaliser Famara Diedhiou had a shot blocked when he might have taken more care with placing his shot.
At the other end Ryan Sessegnon’s clever touch put Tom Cairney away only for him to blaze high over the crossbar.
The second half began with Mitrovic forcing a fine save from Fielding before Reid was just wide from a Diedhiou knock-down.
A crowd of over 21,000 turned up the volume as both teams committed fully to attack again. City’s Ryan Kent was booked for halting a dangerous Fulham break with a cynical trip.
It was rip-roaring stuff, with both sets of supporters, more than 1,600 of them from Fulham, in full cry.
A mistake by City skipper Bailey Wright let in Sessegnon on 69 minutes and a low cross just evaded the stretching Mitrovic.
Back came the hosts, with Kent sending a fierce drive over the crossbar after 72 minutes and Paterson volleying narrowly wide five minutes later.
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