The win also ended the Cottagers’ winless run.
Willian scored to put Fulham 2-1 up before Hwang Hee-Chan lashed in a penalty for Wolves over which there was no debate and seemingly earned them a point.
But there was more drama to come when Harry Wilson tumbled to the ground following a soft challenge from Joao Gomes and Salisbury gave a second penalty against Wolves.
This was in injury time and Willian buried it again to continue his 100 per cent Premier League penalty record – seven from seven.
And on this occasion there was no time for another Wolves reply as Fulham celebrated a much-needed first win since the start of October.
