Rashawn Thomas made 14 of 16 free throws to lead the Islanders with 28 points and 11 rebounds.
Texas A&M-Corpus Christi trailed until Pye hit four straight jump shots for a 45-42 lead with 14:15 left in the second half.
The Cowboys, who shot 50 percent in first half, took a 38-36 lead into the break. Their point production trailed off in the second half, making just 2 of 10 from the floor in the first 10 minutes.
The Islanders (11-3, 2-0 Southland Conference) have won 10 of their last 11 games and are off to their best start in program history.