The impressive Adam turned and finished from close range in the 26th minute to register his second goal as a Potters player.
His first was the decisive strike in the previous home match, the 1-0 win over QPR on November 10, and Stoke are now unbeaten in 13 games on their own turf in the league stretching back to February.
Tony Pulis' side, who were the better team overall this afternoon and nearly had another goal when Ryan Shawcross headed against the bar, now have three victories to their name this season and are up to 11th in the table on 16 points.
Fulham, meanwhile, stay ninth and are now winless in their last five games.
Robert Huth headed the clearest early opportunity wide from Matthew Etherington's corner on the quarter hour-mark and the Potters continued to pressurise, with Adam sending the ball over after juggling it in the area.
The hosts kept up the momentum as Glenn Whelan tried his luck from the edge of the area, drilling wide, and Shawcross almost made it 2-0 in the 36th minute when he clattered a header against the bar.
Stoke substitute Kenwyne Jones thought he had doubled his side's lead in the dying moments, but was flagged offside.