The result left Fulham in 18th place on 11 points from 15 games, while Southampton dropped to eighth spot on 25 points.
Fulham threatened to break the deadlock through early counterattacks led by Andre-Frank Anguissa and Ademola Lookman while Southampton captain James Ward-Prowse's free kick in the 26th minute smashed the woodwork.
Long, who led the Southampton attack in the absence of the injured Danny Ings, found the net with 15 minutes remaining but the goal was ruled out for offside.
Defeat, however, would have been harsh on Fulham, who dominated for long periods in the absence of manager Scott Parker, who was self-isolating.
They remain in the relegation zone but now find themselves on a four-game unbeaten run in the competition.