Purvis scored 15 of his 19 points after halftime, Hamilton had 17 points and 10 rebounds and the No. 9 seed Huskies (25-10) advanced to the second round of the South Region.
Josh Scott had 23 points and 11 rebounds for the No. 8 Buffaloes (22-12), finishing 0-3 in the NCAA Tournament in his career. He had five of Colorado's 11 misses in 30 free-throw attempts, aiding UConn's comeback. The Huskies were a 22-23 from the free throw line.
Another 8-0 Husky run pushed the second-half scoring to 30-12 in favor of Connecticut with 7:45 left.
At the break, Omar Calhoun and Jalen Adams led the way with five points apiece for UConn, and Hamilton and Amida Brimah each have four rebounds.
Hamilton had his 12th double-double of the season. The rest of the team has two combined.
The Buffaloes led by as many as 11 points late in the first half over Connecticut, but they also missed 10 of their first 18 free throws. That allowed the Huskies to hang around — and a 24-6 run midway through the second half put them firmly in front.