Black connected on 8 of 13 shots and Johnson was 7 of 13 from the floor, helping the Tigers (6-2) shoot 52.1 percent for the game (37 of 71).
While the Governors managed to shoot 50 percent (24 of 48), they committed 28 turnovers. Memphis committed 23 turnovers.
Memphis was never threatened after a rally before the midway point of the first half erased an early Austin Peay lead.
Memphis forced 17 Austin Peay turnovers in the first half to help the Tigers build a 43-30 lead at intermission.
No Memphis player was in double figures as the Tigers shot 58.1 percent (18 of 31). And while Memphis committed 13 turnovers, it seemed minor compared to the Governors.
Austin Peay was 11 of 19 from the field (57.9 percent), but the turnovers prevented them from getting any momentum.
And, if not for Betran, things would have been much worse. Betran hit six of his seven shots in the half, part of scoring 18 of the Governors' 30 points.
Austin Peay held an early lead, but after the first media timeout, the Tigers started a 17-2 run that included 13 straight at one point, building the Memphis advantage to 23-10.
The Tigers eventually would extend the lead to as many as 17 with 8 minutes left in the half.
Memphis maintained a sizeable advantage throughout the second half, the lead eventually reaching 21 in the final 5 minutes.