Referee Graham Salisbury made himself unpopular with the Leeds crowd by rejecting three penalty claims before midfielder Pritchard pounced beyond the far post, finishing off clever approach play down the right by substitute Jon Toral and Toumani Diagouraga.
Salisbury quickly imposed his authority on a keenly contested affair, showing Brentford defender Harlee Dean a yellow card for impeding Billy Sharp, who was recalled to Leeds’ attack after his late winner against Huddersfield a week earlier.
Luke Murphy’s 25-yard free-kick was deflected over the bar and from Murphy’s in-swinging corner Liam Cooper and Sol Bamba narrowly failed to connect.
Andre Gray should have seized an 18th-minute lead for Brentford but after giving Bamba the slip and sprinting through the middle into the penalty box, the Bees’ leading scorer had his shot blocked by alert goalkeeper Marco Silvestri.
Cooper was then fortunate to escape with a yellow card for impeding Pritchard when clean through. Pritchard’s free-kick caused Silvestri no anxiety, but the Leeds keeper needed to be quick to close down Jota as the home defence was exposed once more.
Keen to impress after knocking at the first team door, Sharp fashioned an immaculate cross from the right, which caused Dean to slice just outside his own post.
Leeds’ first penalty appeal came after 42 minutes as midfielder Rudi Austin stumbled after a shove from Moses Odubajo.
The official was loudly booed by angry Leeds fans as he left the field at half-time and again on his return for the second half but, when Austin again went down in the box under a 49th-minute challenge from Odubajo, he again refused to point to the spot.
Nor was he inclined to change his stance when Sharp became the latest Leeds player to make an unsuccessful penalty claim just before the hour mark.
Pritchard’s 64th-minute goal had Leeds fans chanting “one, nil to the referee” and the Bees’ advantage almost doubled with 15 minutes left when Toral smacked a rasping shot against a post.
Leeds’ best chance of the second half fell to Sharp who hooked his shot wide when Austin’s cross was cleared to him.
Albanian striker Edgar Cani left the Leeds bench for his debut four minutes from time and there were some anxious moments for the Bees in stoppage-time as their defence came under siege but they held on.