North Carolina State held Miami scoreless for a 3-minute stretch early in the second half to break things open.
Purvis and Howell both had 16 points with Howell adding eight rebounds. Lorenzo Brown added 15 for the Wolfpack, C.J. Leslie had 11 and Scott Wood and Thomas de Thaey had 10 each.
North Carolina State is coming off its first NCAA Tournament appearance in 6 years.
Miami was led by Allen Roberts and his 16 points.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff