Sethi scored 132 off 258 balls as Services put on board 381 in reply to Goa's 304.
The hosts resumed at 219 for four with Sethi batting on 59. He lost his partner Anshul Gupta (125), who could only 10 runs to his overnight total.
The 21-year-old Sethi went on to score his maiden hundred, which had 13 shots to the boundary ropes.
Goa were 26 for no loss in their second innings in 14 overs as the match ended in a draw.
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