Dimi Konstantopoulos made his first appearance of the season, back on his old stamping ground at Victoria Park.
On an afternoon when it was cool when the sun was up, temperatures plummeted when it set as both sides set about ending the game on top on this qualifying group.
Konstantopoulos wasn't overworked in the early exchanges as Boro's defence dealt with lively work in front of them.
The home side almost took lead when a Niall McGoldrick header looked destined to find the target only for Joshua Smile to head off the line.
It remained a game of few chances until three minutes from the break when a cracking left foot volley from Jon Dagur Thorsteinsson flew through a crowded box and into the bottom left-hand corner of Konstantopoulos' net.
It was Boro with the first opportunity of the second half when Alex Pattison drilled in a low shot from outside the box. The effort was blocked but the ball looped up allowing Junior Mondal an opportunity to head for goal, but he couldn't get sufficient purchase to cause a problem.
It was Fulham with the next chance as Mattias Kait cut in from the left and fired low, but with not enough sharpness to bother Konstantopoulos.
The Boro goalkeeper was in the thick of the action a few minutes later when he saved what looked a certain goal when a defensive slip left Joshua Walker in front of goal. But he delayed his shot and Konstantopoulos did the rest, racing off his line to play his part as the danger was cleared.
In between the chances, Boro fans got their first look at Mikael Soisalo, the 18-year-old Finn who signed in the first week of January.
His first touches were encouraging, but it was Fulham who were next on the scoresheet when Jonathan Burn handled inside the penalty area and George Williams scored from the spot.
Jordan McGhee, set up by Soisalo, saw a low shot saved, then Boro were handed a way back into the game when the referee spotted handball in a crowded box and Arnel Jakupovic drilled straight down the middle from the spot.
The closing minutes brought chances at both ends with Konstantopoulos twice saving from Williams and Cooke seeing a thunderous shot deflected off target.
Scorers Thorsteinsson 42, Williams 75 (pen), Jakupovic 84 (pen).
Middlesbrough Konstantopoulos; McGhee, Fry, Burn, McGoldrick, Tavernier, Tinkler, Pattison (Soisalo 72), Jakupovic, Cooke (Capt.). Mondal (Maloney 60). Subs: Pears (gk); Fewster, Liddle.
Fulham Joronen; Sessegnon, Opoku, Smile (Capt.), Davies, Jenz, De La Torre, Kait, Walker, Williams, Thorsteinsson (Kwietniewski 51). Subs: Ashby-Hammond, Rodriguez.
Referee Martin Coy
Boro Cooke 56, foul.
Fulham Davies 30, foul; Sessegnon 59 foul; Walker 90, failing to retreat.