Seth Curry added 15 points and surprise starter Tyler Thornton had 13 for the Blue Devils.
They shot 51 percent while holding the Panthers to 37 percent shooting and keeping them without a field goal for 5 minutes during the run early in the second half that propelled them to their 31st straight home-opening victory.
Next up for Duke: A showdown with third-ranked defending national champion Kentucky in Atlanta on Tuesday night.
Devonta White had 19 points while R.J. Hunter scored 14 to lead Georgia State.
The Panthers never got closer than 12 points in the second half and turned it over 16 times while being denied their first victory over an Atlantic Coast Conference team besides Georgia Tech.
They threatened to make things interesting shortly after halftime, pulling to 40-28 on Manny Atkins' three-point play with 17:46 left.
Thornton followed with a 3-pointer about 20 seconds later, before adding a steal and layup to stretch the lead to 45-28. Curry capped the run with a 3 from the left wing that made it 52-30 and pushed the lead into the 20s.
The Blue Devils, who had 15 turnovers, gave themselves just enough of a cushion for their 95th straight nonconference victory at Cameron Indoor Stadium, their 13th season-opening victory in a row and their 28th consecutive win against current Colonial Athletic Association members.
Thornton wasn't even expected to be in the starting lineup. Projected point guard Quinn Cook began on the bench along with redshirt freshman forward Alex Murphy, who had been penciled into the role filled through the years by Kyle Singler but wound up sitting out.
Only eight players saw the court for Duke—and only seven played at least 10 minutes. For much of the way, none was more important than Plumlee.
The 6-foot-10 senior nearly had his 19th career double-double by halftime, racking up 10 points and eight rebounds at the end of an opening half in which the Blue Devils trailed for less than a minute early but struggled to generate much separation.
Plumlee blocked two 3-point attempts by Hunter during the 13-2 spurt late in the half that put Duke up by 13. His steal and layup with just under 3 minutes before the break pushed the lead into double figures for the first time at 28-17.