Striker Andrew Johnson laid the ball into the path of McAnuff who slotted the ball past goalkeeper Neil Sullivan with a low shot just before half-time.
Leeds' best chance came through Rob Hulse, but his header was parried by goalkeeper Gabor Kiraly.
Crystal Palace boss Iain Dowie on automatic promotion:
"It's never too late when it's statistically possible.
"Sheffield United are still in the box seat because they've got points in the bag and that's important at this time.
"But we've got to play them and (third-placed) Watford and if we win those, the picture changes."
Leeds: Sullivan, Kelly, Butler, Kilgallon, Crainey (Beckford 77), Miller, Douglas (Bakke 85), Derry, Lewis, Healy (Blake 62), Hulse.
Subs Not Used: Bennett, Moore.
Booked: Kilgallon, Kelly.
Crystal Palace: Kiraly, Boyce, Ward, Fitz Hall, Leigertwood, Riihilahti, Watson, Hughes, McAnuff (Reich 90), Johnson, Morrison (Soares 74).
Subs Not Used: Popovic, Freedman, Speroni.
Goals: McAnuff 43.
Ref: P Joslin (Nottinghamshire).