Shamim and Mukesh headed to a playoff after finishing the regulation 72 holes with matching totals of 12-under-276.
S Chikkarangappa of Bangalore finished third with an aggregate of 11-under-277.
Shamim (66-70-70-70), who was in third position overnight placed three strokes behind the leader Mukesh, made a solid start to the day with pars on the first eight holes and followed that up with a birdie on the ninth.
He landed his approach shot from 115 yards to within a foot of the pin on the ninth. The 34-year-old reigning Rolex Rankings champion went two-under for the day with a birdie on the 14th after landing his chip within three feet of the hole.
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However, there was a reversal of fortunes over the next two holes as Shamim birdied the 16th and Mukesh bogeyed the 17th.
Shamim's second shot from 200 yards stopped just six inches from the hole on the 16th and led to a birdie while Mukesh played a poor chip to bogey the 17th.
The two players headed for a playoff after being tied at 12-under at the end of their rounds.
The first playoff hole (18th hole) turned out to be the decider as Shamim made par and Mukesh dropped a bogey. While Shamim found the green in three shots and made a two-putt, Mukesh missed the fairway and couldn't convert a three feet par putt.