Johnson had opened the scoring for the hosts after just four minutes with a close range strike, after good link-up play with Bobby Zamora, to calm any pre-match nerves the home fans were feeling.
That was it as far as the first half was concerned but it was not long in to the second that Fulham doubled their lead.
Clint Dempsey was the man who settled Fulham nerves with a 20 yard drive that left the Perm 'keeper with no chance, just six minutes after the break.
Damien Duff came on for his debut soon after and made an immediate impact for his new side following his move from Newcastle during the week.
The Irishman set up Zamora within seconds of coming on as a substitute and the striker made no mistake to give Fulham a comfortable lead.
However a goal from Vitali Grishin will ensure it will be a nervy second leg for the Premier League side as it leaves Perm needing just two goals to progress to the next round.
The visitors were unlucky not to score more as it took a fine stop from Mark Schwarzer early in the second half to keep out Martin Kushev.
The minnows seemed inspired for much of the second period and it took a desperate clearance from Zamora and another good stop from Schwarzer to deny them a route back in to the tie.
Fulham had started much the brighter and could have gone in at half-time home and dry. Both Johnson and Dempsey were denied by Perm goalkeeper Sergey Narubin, while Zamora was a constant threat to the visiting defence.