Despite a spirited second half performance, the Bangalore outfit were undone by poor markmanship that included a missed penalty in the closing stages of the contest at the Fr Agnel's Ground in Vash, Navi Mumbai.
HAL held the edge in the initial stages with serious inroads into the rival half by using the flanks to deliver some good crosses into the opposition penalty area.
The visitors' persistence finally paid off late in the game when the referee awarded them a penalty after a Mumbai FC defender was penalised for having handled the ball inside the area. But a spectacular save by the keeper from the resulting spot-kick kept the score deadlocked.
With the game heading towards a stalemate, Mumbai FC orchestrated one final attack which resulted in medio Rodrigues finding himself with enough space inside the penalty area to strike a low shot past the HAL keeper and into the far corner of the goal.
The win enabled Mumbai FC move into second place in the standings - below leaders and local rivals Air India, who recorded a 2-0 win earlier in the day.