Tickets for the fixture were put on general sale yesterday morning and the speed of business prompted Leeds to open the upper section of the East Stand.
The top tier of the stand has not been used for a football match since May 5, 2006, when a crowd of 35,239 watched Leeds draw 1-1 with Preston North End in the first leg of their Championship play-off semi-final.
Ken Bates revealed earlier in the season that the closure was saving the club £90,000 in annual business rates, but the upper tier was opened for rugby
league's World Club Challenge match between Leeds Rhinos and Melbourne Storm on February 29.
It is understood that United are now required to pay business rates regardless of whether the upper tier is used or not as a result of a change in tax relief rules.
A statement from the club said: "The decision has been taken following an overwhelming demand for tickets for our final home game of the season. Tickets for the game went on general sale on Wednesday morning and almost 4,000 were snapped up in less than 12 hours."