Both players finished the regulation 72 holes 18-under par 270, six strokes ahead of Sweden's Rikard Karlberg. Carlos Pigem of Spain, Swiss Martin Rominger and India's SSP Chowrasia finished tied fourth.
Rashid went for an aggressive all-or-nothing approach shot from the fairway after his tee-shot to place the ball 20-feet away from the pin. He missed the 20-feet eagle putt but still made a birdie.
Siddikur, on the other hand, took three shots to reach the greens and could only make the par after missing out of a 10-feet birdie putt. He carded three-under 69 in the final round.
"This is a special win for me because it came at my home course. I had lost last year. So it was really important," said Rashid, who managed a final round of 71.
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"The way I played on the first day, I was confident but Siddikur played very well last two days and at the end the title came in a play-off. I am happy," Rashid, who became richer by USD 54,000, added.
He had lost the title to Anirban Lahiri in a play-off last year here playing on PGTI card.
Karlberg (71, 70, 67) whose both Asian tour wins came at the Delhi Golf Club during the SAIL Open and Indian Open in 2010, carded a four-under 68. Pigem (69, 71, 69), who had finished 21st place in the last edition, also turned in a 68 to total 11-under 277.