The Indian side went into the teams' quarter-final second-leg meeting with a 1-0 aggregate lead, but saw their advantage cancelled out after just 23 minutes.
However, they recovered well to book their place in the last four, maintaining their unbeaten record in the competition at the same time.
Midfielder Edward Wilson was the man to break the deadlock at the Haji Agus Salim Stadium, capitalising on a poor goal-kick to finish well and level the tie overall.
Just short of the interval, Bengal were dealt a further blow as Ryuji Sueoka, who had scored the winner in the first leg, was substituted due to an injury.
But, as with the first leg in India, it was a substitute who got the vital goal for Bengal.
Sueoka's replacement, James Moga, got on the end of a deep Baljit Sahni cross 12 minutes from time to head home and put the visitors in the driving seat.
While Padang rallied late on as they sought to stay in the competition, it was to no avail as Marcos Falopa's men held on to progress to the semi-finals.
Falopa's side will face either New Radiant or Kuwait SC for a place in the final.
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