Thoi Singh (44th) gave Bengaluru the lead but Eric Brown equalised for the hosts from the spot in the 54th minute at the Kalyani Stadium encounter.
But an own goal from Dhanachandra Singh (61st) and an 89th minute strike from India captain Sunil Chhetri gave the Ashley Westwood coached Bangalore side their fourth away win as they brightened their title hopes.
The result keeps United SC very much in the relegation zone as they remain only on five points above bottom-placed Churchill Brothers but have played two more games.
Bengaluru started taking control of the match after the hour mark and showed more purpose going forward. They had the first real attempt of the game when Sean Rooney tested United SC custodian Jayanta Paul while Chhetri also had a penalty claim denied.
The visitors' strong finish to the half was rewarded with a goal after a fine team move. Rooney and Chhetri exchanged passes before the Australian found an unmarked Thoi, who scored from close range.
The table leaders raised their tempo with Chhetri going close with a volley. They regained their lead just after the hour-mark when a Rooney header went into the back of the net after taking a deflection off Dhanachandra.
Despite going in front, Bengaluru continued to attack and Rooney found himself free inside the box but his shot was saved by Paul while Chhetri's effort from the rebound was cleared of the line by Bello Rassaq.
Both sides made plenty of changes in the final 15 minutes with Bengaluru also losing defender John Johnson through injury.
Chhetri finally sealed the issue by capitalising on an error from Dhanachandra and slotting past Paul for his 13th goal of the campaign.
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