Carter finished with 19 points on 9-of-12 shooting, to give him 1,317 for his career. The senior also had 16 rebounds.
Jeremiah Bowman added 17 points, David Robinson chipped in 13 and Jan van der Kooij grabbed 13 rebounds.
The Lancers (1-1) shot 50 percent from the field (33 of 66), thanks in part to 44 points coming in the paint. They were also successful from the outside, hitting 10 of 25 3-pointers, with Robinson going 3-for-5.
Justin Morris led the NAIA Cobras with 23 points, going 5-for-9 from 3-point range. Joshua Hart chipped in 12 points and Marquette Knight added 12 rebounds.
Virginia Intermont outrebounded the Lancers 47-44, but made just 37.3 percent from the field (25 of 67).