At stumps on day one, Patel was steady on his fourth first-class century with Yashpal Singh unbeaten on 4 to put Tripura in comfort zone at 305 for two after Himachal Pradesh skipper Rishi Dhawan put them in.
Dhawan's decision to bowl on a flat Bengal Cricket Academy pitch backfired as their bowlers got little assistance with Tripura batsmen going about their tasks with ease.
Their solitary moment of joy came in the 15th over when Pankaj Jaiswal castled Udiyan Bose (40). The opener was looking fluent with six boundaries and one six in his 46-ball knock before being bowled by the seamer.
Ghosh completed his second first-class century off 188 balls and went on to better his previous best score after tea.
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Patel was slower and completed his fourth first class century from 218 balls.
Dhawan used seven bowlers and it was in the penultimate over of the day that Ghosh lost his focus to be caught by Sumeet Verma off Mayank Dagar, four runs shy of 150.
Brief Scores:
Tripura: 305 for two in 90 overs (Bishal Ghosh 146, Smit Patel 111 batting, Udiyan Bose 40; Pankaj Jaiswal 1/34).