The on-loan midfielder sent Declan Rudd the wrong way from the spot just before the half hour after Bailey Wright hauled George Saville down in the box.
It sealed a comfortable win for the nerveless Bees, and with results elsewhere going their way they ensured there would be no repeat of last season’s final day misery.
Judge stung Rudd’s fingertips after eight minutes and top-scorer Clayton Donaldson was wayward with a string of chances to settle it before the end.
He was brought down in the second half, again by Wright, but Judge slipped as he took the spot-kick at the same end as last season’s finale.
Donaldson also saw a powerful drive cannon against the upright and to safety off the back of Rudd’s head as Brentford pressed for the killer second goal.
Marcello Trotta, last season’s penalty villain, saw an effort blocked on the line with North End’s only worthwhile effort a low angled drive from Craig Davies.