Norwegian Johansen struck after Jarrod Bowen had cancelled out Floyd Ayite’s first-half effort.
Hull came into this game on the back of a disappointing 5-0 defeat Derby last Saturday and they struggled to get hold of the ball early on.
It was Fulham who enjoyed much of the possession and looked to create the chances as Liverpool loanee Sheyi Ojo shot over on his return from an ankle problem while Ayite’s deflected effort nearly caught out Allan McGregor.
Ayite was then denied by a miraculous stop by McGregor from an Oliver Norwood corner, seeing his close-range shot kept out by the Hull keeper.
Neeskens Kebano’s free-kick went just over the crossbar while Ojo side-footed wide again as Fulham dominated.
Hull finally found a foothold and the impressive Bowen came close to a goal on the break when his curling effort just missed a post.
Fulham were to get the goal three minutes before the break, though, and it was their pace that created the chance.
Ojo’s run down the left and cross fell perfectly to Ayite who had the straightforward task of finishing from six yards out.
They missed a great chance for number two within moments of the restart as young left back Ryan Sessegnon headed wide unmarked following Ayite’s cross from the right.
And it was Hull who levelled on 53 minutes through Bowen, who nodded home at the second attempt for his fifth goal of the season after his initial header from Kamil Grosicki’s cross had been saved.
Within seconds, Ola Aina could have turned things around completely, but his shot was cleared off the line by Ryan Fredericks.
Fulham went on to regain the lead on 62 minutes. Ayite failed with a bicycle kick from Fredericks’ cross but Johansen was on hand to fire home the loose ball via the crossbar.
Ayite’s volley was then kept out by McGregor as Fulham pushed for a third while the Hull keeper bravely dived at Tomas Kalas’ feet to deny the central defender.
Ayite then missed the target again after finding space down the left side as Fulham failed to convert their chances.
That forced an unnecessary nervy stoppage-time period of five minutes in which Sessegnon came close to heading into his own net from Grosicki’s cross.
Still Fulham continued to create chances on the break, with substitute Yohan Mollo’s deflected effort coming off the bar.