Oklahoma State advanced to the semifinals of the East Rutherford Region to meet St. Joseph's in what will be a meeting of the top two seeds.
Allen scored 13 of his 23 points in the second half to help the Cowboys reach the 30-win mark (30-3).
The game was tied at 42-42 after a basket by Pittsburgh's Carl Krauser with 7:51 left.
But Oklahoma State answered with a 17-5 run as Allen scored seven points and Graham six. Graham put the Cowboys ahead for good on a layup with 7:22 left.
"The second half, because we could control the boards a little better, we were able to run," Cowboys Coach Eddie Sutton said. "We didn't give up a lot of second shots."
The win was the 20th in 21 games for the Cowboys. Pittsburgh (31-5) shot just 37 percent from the field.