Our Under-23s scored first then had to come from 3-1 down to take their first points of the season.
A cold, blustery wind made life a little difficult at Rockliffe Park, but it took Boro 30 seconds to win a penalty and 41 to convert it as former Fulham player Djed Spence was brought down and Ben Liddle scored from the spot.
A deep cross from Djed Spence was only just out of the reach of Dan Ward and Patrick Reading, but the bright start soon faded as Fulham took over.
Not long after Cody Drameh shot a yard over from the D, the visitors equalised on 13 minutes when Boro failed to clear a free-kick whipped in low from the right-hand edge of the box and Moritz Jenz tucked un from close range.
Fulham edged in front on 32 when Cameron Thompson was first to a loose ball on the edge of the six-yard box after a quick move had Boro scurrying to cover.
Thompson was the provider on 61, doing well to set up Jayden Harris who stroked home.
The comeback started just two minutes later when good work from Billal Brahimi set up Tyrone O'Neill who tucked home from the edge of the six-yard box.
It proved to be the first of three goals in 24 minutes, the second of which brought Boro level.
It came on 74 minutes, set up by O'Neill and finished by Connor Malley, whose half-time introduction had helped turn the game in Boro's favour.
Malley was influential in Boro's fourth on 82 minutes, driving into the box and crossing low for Ward whose shot was deflected in by Tyrone O'Neill.
Boro Hemming; D Spence, Reading, Wood, Stubbs (Capt.), Dale, K Spence (Malley 46), Liddle, O'Neill, Ward, Brahimi. Subs James (gk); Guru, Mahmutovic.
Fulham L Ashby-Hammond; Drameh, Mundle-Smit, Harris, Jenz (Capt.), Atkinson, Hilton, O'Riley, Thompson, Francois, Dagur Thorsteinsson. Subs T Ashby-Hammond, (gk); Davies, Tiehi, Kelly, Carvalho.
Referee Glen Hart
Boro Spence 41, foul; Liddle, 81, foul; Brahimi 85, throwing the ball away