Jharkhand were 95 for three when stumps were drawn after the first day's play at the Maharaja Bir Bikram College Stadium.
Opting to bowl, Yadav returned impressive figures of six for 38 to help the visitors bundle out Tripura cheaply.
Opener Subhrajit Roy was the top scorer for Tripura with a knock of 43.
Jharkhand trailed by just 11 runs with seven wickets remaining in the first innings.
Brief scores:
Tripura 1st innings: 106 in 43.1 overs (Subhrajit Roy 43; Ajay Yadav 6/38)
Jharkhand 1st innings: 95 for three in 30 overs (Ishank Jaggi batting 43 Saurabh Tiwary batting 38).
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