The former Canadian International, who had scored a hat-trick in Mumbai, did an encore with his stunning goals in the ninth, 47th and 83nd minutes before Adrian Mutu (86th) pulled one back for the visitors.
Substitute Dejan Lekic, who was brought in place of Sameehg Doutie, sealed the issue with his goal in the dying minutes (90+4th) for their superb win in front of packed turnout of 48721.
The Antonio Habas-coached thus sealed their second successive last-four berth of the tournament with 23 points from 13 matches and they will face Mumbai City FC in their concluding league match at home on December 4.
FC Pune City (15 from 12 matches), on the other hand, stretched their winless run to seven matches and their chance of progression to semis will now come down to 24.01 per cent, as per an ISL statistic.
ATK took a ninth minute lead when Hume broke Pune's resistance after being set up by Arata Izumi from the left flank.
The assistant referee however did not raise the flag finding Hume on side as the Canadian brought up his seventh goal by slotting the ball into the roof of the net from point-blank range.
Hume brought up his brace, and eighth goal of the tournament, two minutes into the second-half with a brilliant side volley which was equally stunningly set up by captain Borja Fernandez with an outstep scoop and the Canadian had all the time to put it beyond Pune goalkeeper Arindam Bhattacharya.
The bald ATK forward showed superb reflexes to clear a loose ball after it deflected off the post before any Pune player could get hold of it.
