The last time Albion faced the Hatters in a league game at The Hawthorns was in the 2006/07 season.
The Baggies would come out as 3-2 winners in a thrilling game, although it took two late Kevin Phillips goals to secure the points.
Jason Koumas struck the opener just before half-time, but Keith Keane and Warren Feeney both netted to flip the tie in Luton’s favour.
However, Phillips scored a double in the last two minutes of normal time to win the game for Albion.