Shine, who made his first seven shots, was 8 of 11 from the field while Wallace hit 6 of 11 shots and grabbed seven boards. The duo combined to knock down eight three pointers.
High Point (10-15, 6-9 Big South Conference) led 18-15 before Shine scored five unanswered points to put the Panthers up 23-15.
Coastal Carolina (17-7, 10-4) cut the lead to six, 29-23, behind a Sam McLaurin layup but Shine converted two jumpers to give High Point a 33-25 lead at halftime.
The Chanticleers rallied in the second half, this time cutting the deficit to 66-62 with 1:16 left, but Shine stepped up again, knocking down two free throws to give his team a 68-62 lead with 39 seconds remaining.
Kierre Greenwood led Coastal Carolina with 18.