Lenny Rodrigues scored the only goal of the game in the 17th minute. Courtesy the win, Bengaluru jumped to the fourth position with 16 points from 11 matches.
Minerva, who saw their six-game unbeaten run broken, stayed seventh having 11 from 12 games.
Minerva continued with their rotation policy, making as many as six changes to the side that held Mumbai FC to a goalless draw. Bengaluru, on the other hand, had three from the team that lost to league leaders East Bengal 1-3.
Centre-back John Johnson returned to the starting lineup after an injury layoff while Serbian striker Marjan Jugovic making his debut.
It was not an eventful first half despite the away side playing four forwards with Sunil Chhetri, Udanta Singh, C.K. Vineeth and new signing Jugovic all playing.
The only real action of the half was the goal when Cameron Watson floated in a free kick which the tall and wiry Lenny headed in past home keeper Arnab Das Sharma who could only deflect the ball onto the horizontal and into the goal.
Bengaluru attacked with more venom after taking the lead as Chhetri tried to weave his magic against lesser fancied opponents.
The second half had little in it as Minerva failed to conjure up any move of note to level proceedings.
For Bengaluru, Jugovic did not impress and was substituted by Harmanjyot Khabra in the 57th minute.