McBride scored on his third goal of the season, putting away Simon Davies' cross with a half-volley and then had his volley tipped off the crossbar by fellow American Marcus Hahnemann.
Fulham hit the woodwork two more times before Erik Nevland put the game away in stoppage time.
Four Americans (Kasey Keller, Clint Dempsey, sub Carlos Bocanegra and McBride) started for Fulham, and a fifth Cottager (Canadian Paul Stalteri) is a U.S. college product (Clemson).
The Cottagers remain second to last in the EPL with slim hopes of staying up with five games to play.
"We stayed in the race today, and still have a chance," said Fulham manager Roy Hodgson. "What pleased me was that we did it the right way; we played football from first to last."
16. Reading 32 (-26)
17. Birmingham City 31 (-13)
18. Bolton Wanderers 29 (-21)
19. Fulham 27 (-24)
20. *Derby County 11 (-58)