After Young had a basket, Melvin scored on a fast-break layup and followed that with a 3-point play to put DePaul (3-1) up 57-50 with nine minutes remaining.
Young scored 23 and Melvin had 20 in DePaul's 86-85 loss to Minnesota on Thursday.
DePaul, up 71-68, had a chance to secure the game, but Young, with 1 minute to go, and Krys Faber, at the 31-second mark, both missed free throws.
Texas Tech turned the ball over after Faber's miss, forcing a foul that resulted in Melvin connecting on two free-throw tries to make it 73-68.
After Nurse had a 3-point play to get Texas Tech within one, DePaul responded with a 7-2 run for a 68-62 advantage. Jeremiah Kelly made three free throws and Melvin had a base-line slam during the stretch.
Melvin put DePaul up 48-41 with a layup 6 1/2 minutes into the second half. Texas Tech got the next seven points, including five by Terran Petteway, to tie it at 48.
Nurse scored 11 points, helping Texas Tech go up 37-36 at halftime. He had just one point in the Red Raiders' 60-49 loss to Indiana State on Friday.
Young had 15 first-half points, a tight session that had 14 lead changes and five ties. The biggest lead for either team was five points.
The win gave DePaul 1,375 in its history.
This was the first time the two teams have played each other since the 1983 Suntory Ball Classic, which took place in Japan.