Jordan Hugill had sent the R's into an early lead in the English capital, but Kamara scored once in either half to ensure that Fulham, who have moved into fourth spot in the table, would collect all three points.
Fulham entered the match without the services of this season's Championship leading scorer Aleksandar Mitrovic, who missed out though suspension, which saw Kamara start through the middle.
Left-back Joe Bryan and captain Tom Cairney were back into the XI, though, for a team looking to return to winning ways in front of their own supporters having lost to Hull City in their last game at Craven Cottage.
The R's made a bright start to proceedings and took the lead in just the fourth minute when Hugill bundled a low Todd Kane cross into the back of the net from close range.
Play resumed for a moment, but the referee's watch quickly signalled that the ball had crossed the line, sparking celebrations in the away end.
The visitors had a huge chance to double their lead in the seventh minute when Fulham goalkeeper Marek Rodak palmed a strike from Wells into the path of Kane, but the lively defender fired over the crossbar from close range.
Hugill then struck over the crossbar in the 10th minute with QPR having the better of the early exchanges against a Fulham side struggling to get hold of the ball in midfield.
QPR then hit the post down the other end when a low cross from Kane was deflected onto the woodwork by the sliding Tim Ream, before Rodak had to keep out a powerful Hugill drive, all inside 16 minutes.
Kamara's first sight of the QPR goal came in the 19th minute after working some space in the wide area, but the forward's effort was always curling away from the target.
The 24-year-old was not to be denied in the 27th minute, however, as he headed a brilliant Denis Odoi cross into the bottom corner to level the scores.
Fulham came close to taking the lead six minutes later when Ivan Cavaleiro struck a powerful attempt towards the bottom corner after smart work from Cairney, only for the post to come to QPR's rescue on this occasion.
QPR had the better of the early exchanges but Fulham were in control approaching the end of the first period, with another opportunity coming and going when Stefan Johansen sent a free kick into the arms of Lumley.
Rodak made another smart save to keep out an attempt from Hugill in the final exchanges of the first 45, and the two teams headed down the tunnel at 1-1 following an entertaining opening half of action.
The first chance of the second period came for QPR when a half-cleared corner fell for Lee Wallace, but the defender could only scoop the ball over the crossbar.
Fulham took the lead in the 64th minute of the match when Kamara collected a smart pass from Johansen before finding the back of the net despite the best efforts of Lumley.
The home side almost had a third shortly after when Knockaert broke into a shooting position, but the attacker saw his low effort hit the post as QPR survived conceding another.
The woodwork again came to the away side's rescue in the 68th minute when Cavaleiro's low effort struck the foot of the post during a period of dominance.
The chances dried up in the spell that followed, though, and the Cottagers were able to ease their way to their eighth Championship win of the campaign despite five additional minutes, leaving them just four points off leaders West Bromwich Albion.
Next up for Fulham is a home game against Derby County on Tuesday while QPR will attempt to return to winning ways when they host Nottingham Forest on Wednesday.
FULHAM (4-3-3): Rodak; Odoi, Mawson, Ream, Bryan; Reed (Reid 55'), Cairney, Johansen; Knockaert (Christie 76'), Kamara, Cavaleiro (McDonald 90')
QUEENS PARK RANGERS (5-3-2): Lumley; Kane, Hall, Leistner, Wallace, Manning; Amos (Chair 65'), Ball (Mlakar 81'), Eze; Wells (Scowen 66'), Hugillbody check tags ::