Pat Holland put West Ham into the lead in the 28th minute.
In attempting the backpass, Lampard tore a stomach muscle that ruled him out of much of the remainder of the game.
Three minutes into the second-half, François van der Elst scored, assisted by Rensenbrink.
Keith Robson later equalised for West Ham from a cross by Trevor Brooking.
With two minutes left, as West Ham fell apart, van der Elst ran through to score Anderlecht's fourth goal for a deserved victory.