The victory lifted them to the same points tally as second-placed Hull, with a game in hand, to keep them well within touch of an automatic promotion place.
Two early goals from Albert Adomah and Grant Leadbitter settled the contest by half-time to leave Karanka content.
“I told the players after the game against Leeds the way we were playing would mean we would start winning games,” he said.
“Sometimes when we score one goal we have problems scoring the second one. Today we scored two goals quickly and after that the game became easier.
“If we were to win every single game by 2-0, it would not be a problem for me. I know we are going to score goals because we have a lot of good players.
“Adomah played the same game as he did last Tuesday, and when he plays like that he’s one of the best in the league.”
The hosts had the perfect start after just three minutes - Stewart Downing found space on the left to cross into Adomah, who was left alone in the area to head home his seventh goal of the season.
The lead was doubled on 20 minutes when Chris Baird upended David Nugent in the box. Captain Leadbitter sent goalkeeper Andrew Lonergan the wrong way from the penalty spot.
Moussa Dembele was denied by Dimi Konstantopoulos from a spectacular overhead kick six minutes before the break.
The hosts were denied two minutes later with an excellent clearance off the line from Ritchie De Laet, after a header from Michael Madl.
Fulham were reduced to 10 men on 86 minutes, albeit in controversial circumstances. Richard Stearman was shown a red card for fouling substitute Jordan Rhodes - however, the defender had slipped to foul the striker in his own half.
Fulham manager Slavisa Jokanovic acknowledged the two early strikes for Middlesbrough left his side too much to do.
“We tried to be more aggressive. We made a few chances but they were more solid generally and more organised. They deserved their three points,” he said.
“For the sending-off, possibly he was the last player and I don’t know whether he was in a dangerous area.
“It meant that we could not push on for the last few minutes, because we made the important mistakes at the beginning of the game. It’s not a question of him apologising.
“The result is bad, it’s very clear, and we did not make a good performance. We are inconsistent - some days we do a good job and some days we don’t.”