Cali World Games gold medallist Mehta, who had beaten former World champion Peter Ebdon in the previous round, was better at safety play that marked the contest and it helped him especially in the fifth frame when he made up a 40-point deficit before clearing the table after Miah missed the yellow.
Although Mehta's victory was expected, the 27-year-old from Mumbai, ranked 72nd, was made to fight in every frame by the World No.107 Miah, who is playing in his first season on the pro tour.
Mehta took the second frame on runs of 28 and 42 after conceding the first frame 20-97 to Miah, who had lost against the Indian 0-5 in their previous meeting.
Mehta then had the next three frames with a high break of 67 in the fourth, followed by the 27 in the fifth.
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Bangladesh-origin Miah, who was born in England, let go a 40-point lead in the fifth and misjudged a yellow to leave Mehta in position to clear the table.
"It was not an open game and I thought I played solid. My break of 67 in the fourth was crucial as it helped me control the match better. The fifth was a bit scrappy, but I was happy with the 27 clearance under pressure," he added.