First-half strikes from Heidar Helguson and Brian McBride left Boro still without an away win this season.
Mark Viduka grabbed a late consolation goal, but defeat keeps the pressure on Southgate as Boro remain in a relegation battle, while victory for Fulham lifted them up to 11th.
Fulham boss Chris Coleman was forced to re-shuffle his starting line-up after midfielder Claus Jensen failed a late fitness test before kick-off. The Denmark international was just one of six changes to the team which started Fulham's last outing against Blackburn.
Southgate was also forced to make changes after Jonathan Woodgate was ruled out with an ankle injury.
But it was midfielder Stewart Downing who had the first attempt at goal. His curling 20-yard free-kick in the fourth minute sailed narrowly over the crossbar.
Downing was again causing Antti Niemi problems in the Fulham goal just two minutes later. His corner kick looked to be dipping under the bar forcing Niemi to make the save.
Boro looked to make all their early possession count as Downing again forced Niemi to make a save before Mark Viduka headed wide of the post.
James Morrison then got in on the act as he raced through the Fulham defence only to plant his shot straight at Niemi.
Middlesbrough were made to pay for their poor finishing when Helguson put Fulham in front from the penalty spot in the 12th minute.
Referee Mike Dean showed no hesitation in pointing to the spot after Moritz Volz was clipped in the area by George Boateng. Helguson took the resulting penalty and slotted the ball into the bottom right corner as Mark Schwarzer dived the wrong way.
A mistake by Philippe Christanval nearly cost Fulham their advantage though four minutes later. The French defender mis-kicked his clearance to allow James Morrison to sneak in after a neat one-two with Viduka. His shot flashed across the Fulham goalline before being cleared.
The sheer pace of the game would not let up and a slip by Zat Knight allowed Yakubu a clear run at goal but his shot was again palmed away by Niemi.
But once again Boro were punished when former USA international McBride made it 2-0.
McBride was played in by Tomasz Radzinski and allowed time to pick his spot and curl the ball past Schwarzer from the edge of the box as the Middlesbrough defence went missing.
Southgate introduced Lee Cattermole into his midfield after the restart to inject some more creativity.
Boro were definitely more rugged but could not find a break through. Yakubu came close but when he ran into the box he elected to fall to the ground when he should have stayed on his feet.
He made amends though in the 74th minute when he flicked the ball on for Viduka to race clear and slot past Niemi.
The goal prompted Middlesbrough to attack as Fulham found themselves on the back foot and Niemi was forced to make a number of smart saves as Fulham clung on to snatch the points.