The Blasters were hammered 0-5 by Mumbai City FC in their previous match but they returned to winning ways with goals from Duckens Nazon (7th minute) and Aaron Hughes (57th minute).
Anibal Zurdo managed to pull one back for the visitors in the second minute of added time but that came too late for the Pune City.
The victory took Blasters to the third spot with 18 points from 12 matches, the same as Atletico de Kolkata who have a better goal difference. Kerala Blasters now need only a win from their remaining two matches. Kerala will travel to Kolkata next to play ATK on Tuesday and return home to host NorthEast United on December 4.
Losing their second consecutive match, Pune are placed fifth with 15 points from 13 matches and it will be difficult for the team coached by Antonio Habas to qualify with just a match in hand. Habas will have a week's break before they travel to Kolkata to play against his former club on 2 December.
Blasters coach Steve Coppell made several changes to the team that got clobbered in Mumbai with marquee player Aaron Hughes back into the squad, alongside Kervens Belfort, Duckens Nazon, Mohammed Rafi and goalkeeper Sandip Nandy. Pune made three changes to their side but, playing at home, Kerala started the match on the front foot.
The home team took the lead in the seventh minute itself as Duckens Nazon capitalised on a defensive lapse. A goal-kick by Pune goalkeeper Edel Bete saw Hughes win the ball from a header.
Pune defender D Ravanan then failed to control the ball and Nazon, who was lurking nearby, pounced on the opportunity as he raced clear, set aside the challenge of Gouramangi Singh and fired past the Pune goalkeeper.
Pune tried to fight their way back but Kerala were always in control of the proceedings. The pace of Kervens Belfort, Nazon and CK Vineeth was always going to be difficult for Pune City and it was in tune with the proceedings that Kerala enhanced their lead in the second session.
A corner in the 57th minute was only partially cleared by Pune City and Vineeth chased it down on the left, sending a cross to the far post. The Pune defence shockingly stood still, allowing Aaron enough time to rush and head home from point blank range.
The goal crippled Pune City, who however managed to pull a goal back in stoppage time. A cleverly taken free kick saw Pitu touch the ball to set up Anibal Zurdo, who blasted it on to the far post, past goalkeeper Sandip Nandy.
The goal, however, came too late and there was no time for Pune City to get anything out of the match.
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