Karringtonn Ward had 25 points and eight rebounds and Glenn Bryant had 11 points and nine rebounds for the Eagles (5-3), who have lost three in a row.
Scott went 9 of 10 from the free throw line in the final 2:43 to keep the game out of reach, including Purdue's final seven points. Scott grabbed a steal at the end of the game to keep the Eagles from making a final push.
Late in the second half, Basil Smotherman scored on a jumper and Sterling Carter hit a 3-pointer to give the Boilermakers a 50-45 lead before Eastern Michigan's Jalen Ross hit a 3-pointer to put the Eagles within two.
Scott, who started in place of Ronnie Johnson, scored before Bryant answered with a basket to make it 52-50.
With 5:15 left, Johnson hit a 3-pointer, Ross split from the line, and, later, Scott grabbed a steal and was fouled on a lay-up, but missed the extra free throw and the Boilermakers took a 57-52 lead.
Ward hit a 3-pointer to make it 57-55, but the Eagles never could get over the hump.
The Eagles led just once -- a one point lead in the first half when Ward hit a 3-pointer at the 7:26 mark.
Purdue jumped out to a 9-2 lead. Stephens hit two 3-pointers and Terone Johnson hit a shot and Scott split from the line. But the Eagles went on an 8-0 run to get back within a point.
Eastern Michigan's Raven Lee scored twice and Bryant hit two free throws and then dunked to make it 11-10 midway through the first half.
Purdue led 35-29 at halftime.
The Boilermakers built an 11-point lead with a 7-2 run to start the second half.
Scott drove to the basket, Smotherman scored two free throws and Johnson hit another, and Stephens scored on a lay-up and the Boilermakers took a 42-31 lead early in the second half.
Then the Eagles went on a 11-3 run of their own.
Riley scored, Ward hit a 3-pointer and Bryant scored on a jumper and two free throws and Lee scored two more free throws to put the Eagles within three.
Then Ward grabbed a steal and went the length of the floor for a dunk to make it 45-44 with 10:53 remaining.
The Boilermakers shot 40 percent, but just 36.4 percent in the second half and were outrebounded, 39-32.