The Rainbow Warriors (17-10, 7-7 Western Athletic) won their fourth consecutive game and split the season series with the Aggies (14-15, 8-6), who dropped their third straight.
Johnson was 8 of 14 from the field, including six 3-pointers. Joaquim was 7 of 10 from the field and had 18 points and 15 rebounds, while Amis added 14 points and 11 boards.
Amis' layup off Joaquim's assist capped a 16-4 run gave the Rainbow Warriors their largest lead at 58-45 with just under 12 minutes left.
Hawaii led by 11 with 5:43 left in the first half, but the Aggies used a 13-4 run to cut the deficit to 35-33 at intermission.
Christian Kabongo led New Mexico State with 22 points.