Australia had resumed day three of the day-night pink-ball Test on 99-6 but only added 22 runs as Alzarri Joseph took 5-27 for the hosts.
The Windies reply started with left-armer Starc, 35, dismissing John Campbell with the first delivery before he trapped Kevlon Anderson leg-before and bowled Brandon King with his fifth and sixth balls respectively as all three went without scoring.
Starc took out Mikyle Louis, who had scored four, and Shai Hope (2) in his third over to leave the hosts on 7-5 after 4.3 overs.
Josh Hazlewood removed Roston Chase for a duck to reduce the West Indies to 11-6 before Boland’s hat-trick.
The right-armer dismissed Justin Greaves, who top-scored with 11 of the 27, Shamar Joseph and Jomel Warrican in the 13th over.
A misfield allowed West Indies a run with the score on 26 before Starc bowled Jayden Seales to end the hosts’ innings and give him his 402nd Test wicket, while also reaffirming his status as the best exponent of pace bowling with the pink ball in Test cricket.
“It’s been a fantastic series,” said Starc, who became the fourth Australian to pass the 400-wicket mark as he followed Nathan Lyon, Glenn McGrath and Shane Warne in reaching the landmark.
“We’ve seen some difficult batting conditions throughout but a fantastic series for us. It’s been a good few days, really enjoyable. I go home with a smile on my face.
“Our bowling attack has been pretty on the money throughout the series and today was another case of that.”
The teams will contest a five-match T20 series next, which begins on 21 July in Jamaica (01:00 BST).