In search of their fourth win on the trot, Aniket Choudhary (4-34) and Tanvir Mashrat Ul-Haq (3-39) wreaked havoc on the Uttar Pradesh batsmen as wickets kept tumbling at regular intervals.
Choudhary, a left-arm medium pacer, ran through the UP top-order as the hosts were reduced to 36-4 at one time.
But then Haq bowled Raina to break their fledgling resistance. Haq also sent Rinku Singh and Saurabh Kumar back to the pavilion.
At stumps, Upendra Yadav (21 not out) and Shivam Mavi (9 not out) held fort as the hosts still trailed Rajasthan by 165 runs.
Earlier, Rajasthan rode on Robin Bist's valiant 96 and equally effective 93 by opener Amitkumar Gautam to post a competitive 311/9 in their first innings.
Bist, who retired hurt on 68 Wednesday, resumed his innings Thursday, and added 28 runs to his overnight tally. But the batsman again retired hurt Thursday.
Meanwhile, Assam are in sight of an outright win after they bundled out Haryana for a paltry 97 in the first innings and reduced them to 78/7 on follow-on in the second essay after putting a respectable 310 in their first innings.
For Assam, right-arm medium Arup Das has picked up nine wickets in the match so far.
Rasool was unbeaten on 53 in J&K's second innings, but his side still trailed by 42 runs.
Brief scores: At Kanpur:Rajasthan 311/9 (Robin Bist 96 retired hurt, A V Gautam 93, Ankit Rajpoot 5-61) versus Uttar Pradesh 146/7(Suresh Raina 33, Rinku Singh 31, Aniket Choudhary 4-34). Uttar Pradesh trail by 165 runs.
At New Delhi (Palam): Jammu and Kashmir 95 and 115/6 (Parvez Rasool 53 not out, Diwesh Pathania 3-24) versus Services 252 (Aanshul Gupta 59, Navneet Singh 58, Parvez Rasool 8-85). Jammu and Kashmir trail by 42 runs.
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