The victory has now made automatic promotion to the Premier League look likely for Brian McDermott's side.
Federici had to pull off a smart save soon after when Adam Llalana's shot had taken a deflection through a crowd of bodies in the area.
Llalana had two more efforts before 15 minutes had even been played, but Federici was again equal to them.
The Saints nearly drew themselves level before the break, but Jos Hooiveld could only put his free header wide from a corner before Lambert floated his header over.
Southampton came out flying for the second half, and they drew themselves level in the 48th minute when Lambert's deflected effort hit the back of the net.
Richard Chaplow's shot was gathered by Federici soon after, while Lambert was again on the prowl as he dragged his effort wide.
Despite the home side controlling the flow of the game, Reading again delievered the killer blow against the run of play.
This time it was substitute Adam Le Fondre who powered the ball into the roof of the net from Kebe's pull back with 15 minutes to play.
The win was sealed in injury time when Le Fondre capitalised on some slack defending from Jose Font before slotting in.
The league leaders are now nine points clear of the playoff places with three games left to play.