Taylor made four of the Thundering Herd's final eight points in the first half for a 28-24 lead at intermission, and Marshall stretched it to nine points at the start of the second.
Rice's Bishop Mency made back-to-back 3-pointers to close within 33-30 with 18 minutes left to play. Taylor then sparked a 10-0 run with eight-straight points, and the Thundering Herd took a double-digit lead that they never relented.
Taylor finished with seven assists, Austin Loop chipped in 16 points and JP Kambola added 10 points for Marshall (7-16, 3-7 Conference USA). The Thundering Herd shot 52.9 percent from the floor and 10 of 25 from distance.
Mency scored 13 points to lead the Owls (6-15, 3-6).