However, the home fans didn't have long to wait for the opening goal. A corner was flicked on and Rickie Lambert rose to nod the ball home.
© Getty Images
It was almost two just minutes later, but Stekelenburg was able to keep out Jay Rodriguez's shot.
Rodriguez then went close again with a header from 12 yards. Fulham, however, failed to register a shot on target in the opening 30 minutes.
Southampton's pressure continued and Lambert almost grabbed his second with a low drive that clipped the post.
Stekelenburg then had to be alert to deny Lambert again. This time the striker managed to reach James Ward-Prowse's cross, but the Fulham goalkeeper was equal to it.
There was little he could do about the Saints' second, however, as Rodriguez nodded in Lambert's cut back after Lallana had whipped the ball in.