Peter Handscomb and Matthew Renshaw each notched their second half-century of the match as the Prime Minister's XI set up a challenging fourth-innings chase for the West Indies in the four-day pink-ball game at Manuka Oval.
At dinner on day three, the home team was 3-164, a lead of 251, with Renshaw on 71 and captain Josh Inglis on two.
Handscomb, who scored 55 in the first innings, was bowled five minutes before the break by spinner Kraigg Brathwaite for 75 off 138 balls.
He dealt confidently with an early bumper barrage and struck six fours, adding 145 for the third wicket with Renshaw after the West Indies had reduced the home team to 2-13.
Handscomb did give a couple of chances, dropped at second slip on 41 and short point at 54.
Renshaw, who top-scored with 81 in the PM XI's first innings, struggled for touch early on and notched just one four off the first 88 balls he faced.
He played with more fluency as the innings progressed, with seven fours to his name by the dinner break.
Paceman Alzarri Joseph (1-32 off 11 overs) was the most consistently challenging of the West Indies bowlers.
Resuming at 7-234, the West Indies added just one run from a no-ball before their innings ended in the second over of the day.
Paceman Mark Steketee (3-33) trapped Alzarri Joseph lbw for 14 and two balls later Jayden Seales (0) was well caught at second slip by Handscomb.
With Raymon Reifer unable to bat, the West Indies ended on 9-235, a deficit of 87.
Left-arm quick Joel Paris (3-32) and spinner Todd Murphy (3-27) were the other main wicket-takers.
By the time the PM's XI had got their lead to 100 they had already lost two wickets.
Marcus Harris (5) edged a Seales delivery into his stumps and Henry Hunt (2) was caught behind slashing at a Joseph delivery.
