Despite the lack of goals at the John Smith's Stadium, the second leg of the semi-final tie proved to be an absorbing affair, both clubs having their chances to establish a narrow lead after the opening fixture at Kenilworth Road had ended 1-1.
However, moments after seemingly being denied what appeared to be a clear penalty, Huddersfield scored the only goal of the game in the 82nd minute through substitute Jordan Rhodes.
A free kick from fellow replacement Sorba Thomas found the forward at the back post, and the 32-year-old was able to get ahead of his marker to prod the ball home.
Although they had more than matched their hosts throughout the contest, Luton faded during the closing stages, leaving Huddersfield to earn their place at Wembley Stadium on May 29.
Carlos Corberan's side will square off against either Nottingham Forest or Sheffield United, the former holding a 2-1 advantage heading into Tuesday's second leg at the City Ground.