Johansson got the faintest of touches on Gareth Williams' corner after 10 minutes to put the Foxes ahead and the lead was defended comfortably.
Leicester dominated and they enjoyed the better of the early exchanges in what was an open contest throughout
Cardiff barely threatened until Paul Parry's low drive from 25 yards somehow missed the target.
Leicester boss Craig Levein:
"For 85 minutes we were comfortable which is some feat in a difficult place like Cardiff.
"In the last five minutes they threw everything at us and we have Paul Henderson to thank for three fantastic saves in the dying minutes.
"Cardiff had only lost one of their last 12 matches so it's fantastic."
Cardiff: Margetson, Weston (Ardley 74), Purse, Loovens, Barker, Parry (Ferretti 82), Whitley, Ledley, Koumas, Lee, Jerome.
Subs Not Used: Alexander, Darlington, Cox.
Leicester: Henderson, Maybury, McCarthy, Gerrbrand, Johansson, Gudjonsson, Williams, Hamill, Tiatto (Kisnorbo 84), Dublin (de Vries 78), Hammond.
Subs Not Used: Douglas, Sylla, Sheehan.
Goals: Johansson 11.
Ref: I Williamson (Berkshire).