Both Smith and Armstrong hit half their shots to boost the Wildcats, who shot just 34 percent. Leading scorer Tanner Leissner was only 3 of 13 for nine points with nine rebounds. Ronnel Jordan, who had scored 16-plus points in three straight games, left with a first-half injury.
The Wildcats (8-6, 1-0) trailed 34-33 before outscoring the Bearcats 25-9 over the final 10 minutes. In that stretch, Smith, coming in as the nation's co-leader in free-throw percentage at 95.4, was 6 of 6 from the line with two baskets.
Willie Rodriguez notched his third double-double this season with 20 points and 11 rebounds for the Bearcats (3-12, 0-2), who shot 36 percent and were 3 of 20 on 3-pointers.
UNH won its conference opener for the first time since 2007-08.