Chencho smashed the second goal for Bengaluru in 71st minute after United striker Federico Gallego got the equaliser in the 60th minute.
Bengaluru will still be on their guard as they are challenged by the next best side, NorthEast United FC at the Indira Gandhi Athletics Stadium.
Ogbeche has now equalled Ferran Corominas' tally of eight goals in the race for the Golden Boot.
Arnold Issoko's fourth-minute goal was the difference between the two sides as the Islanders climbed to third on the table with 13 points from seven games.
A moment of individual brilliance from Federico Gallego (82nd minute) and a clinical strike by Bartholomew Ogbeche (90th) helped NorthEast United climb to the top of the table with 11 points.
Bartholomew Obgeche (20th minute) gave the hosts early lead before Farukh Chaudhary cancelled out his strike in the 49th minute.
Bartholomew Ogbeche was the star for the Highlanders with a stupendous hat-trick, which helped the visitors neutralise Chennaiyin FC's advantage.
After an away loss to Bengaluru FC in their campaign opener, Chennaiyin were outclassed by an attack-minded FC Goa at home on October 6.
The home side, who kicked off the fifth ISL season with a 0-2 loss to Kerala Blasters, were reduced to 10 players in the 32nd minute
Ferran Corominas (14th, 38th) bagged both goals for the visitors while Federico Gallego (8th) and Bartholomew Ogbeche (53rd) were the scorers for the hosts.
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For four successive years, NorthEast United FC have tried but failed to win a place in the playoffs.
Romanian Goian, who was the villain in the first half after conceding an own goal to allow North East take a 2-1 half-time lead, finally made amends in the dying minutes.
It was Marcelinho who got the goal that Pune were hunting for all night and came when the visitors had pulled out their top scorer Emiliano Alfaro.
Captain Sunil Chhetri, once again gave the hosts the much-needed lead, after they had conceded an equaliser just before the first half.
NorthEast United had lost 0-3 against Chennaiyin FC in Chennai earlier in their first-leg clash but Doungel turned the tables on their rivals with a hat-trick.
Zequinha was the star of the show, striking in the 73rd minute to give his side the lead and the winner.
Brazilian striker Marcelinho scored a fabulous hat-trick after Ashique Kuruniyan had opened the account in the eighth minute and Adil Khan hammered the final nail late in the game as Pune City took a giant leap in standings.
Balwant Singh scored on either side of half-time to ensure a 2-0 win for the Mumbai outfit over the unlucky hosts NorthEast United FC.
Blasters started well and put persistent pressure on their rivals as the visitors lost their goalkeeper in the first half of the match.
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