The Nittany Lions (12-10, 3-6 Big Ten) got 19 points from Newbill, 18 from Frazier and 15 from Taylor.
Taylor scored nine points down the stretch, enough to keep Purdue at arm's length.
Despite committing some late turnovers that allowed the Boilermakers to remain in the hunt, Penn State went 11 for 12 from the free-throw line in the final 1:07. The Boilermakers missed shots underneath the basket and were forced to foul.
Penn State, which started conference play with a six-game losing streak, recorded its first three-game conference winning streak since the 2008-09 season.
Taylor also pulled down eight rebounds for the Lions and Frazier had seven as Penn State controlled the boards by a 40-36 count.
The Boilermakers pulled to within 34-29 at the half, then started the second half by drawing the third foul each of Penn State's Frazier, Taylor and Donovon Jack.
But the Lions' balanced scoring continued as John Johnson sank a pair of free throws, Taylor popped a long 3-pointer and Frazier completed a coast-to-coast drive for a 10-point advantage at 51-41.
Purdue's Hammons and Errick Peck answered with eight straight points to pull within two, but Penn State recovered when Frazier sank two foul shots, Newbill drove uncontested for a layup and Johnson scored on a nifty reverse layup to build back to an eight-point lead.
Penn State used a 21-4 run in the first half to rally from a 14-7 deficit to a 28-18 lead.