A 3-pointer by Tellinghuisen with 7:40 left gave South Dakota State its biggest lead, 71-61.
Idaho slowly climbed back into the game, pulling within two, 84-82, when Mike Scott hit a 3 with 1:19 remaining.
Bittle made a layup on the other end before another Scott 3-pointer made it 86-85 with 34 seconds to go.
The Vandals were forced to foul and Parks made 1 of 2 free throws 9 seconds later.
Scott and Sekou Wiggs each missed shots in the waning seconds.
Idaho (4-5) shot a season-high 60 percent (29 of 48) from the field, but committed 18 turnovers.