UP, who resumed at 270 for eight, were all out for 291 in the morning.
In response, Delhi were looking good at 125 for one before Gautam Gambhir's fall triggered a middle order collapse, which saw the team in serious trouble at 187 for five.
After Gambhir (86), Dhruv Shorey (65 not out) held the innings together but Delhi still need 63 runs to equal UP's first innings total.
While Delhi pacers reveled on a green surface on day one, UP spinner Kumar (3/74) came up with crucial breakthroughs.
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The former Delhi captain played solid and hit 13 fours during his 122-ball innings.
Milind Kumar was out for a duck, leaving Delhi at 127 for three. Shorey and Rishabh Pant (30) got together but were not able to build a big partnership that was needed to change the momentum of the game in the home team's favour.
Pant, playing his first game of the tournament, batted like he normally does hammering three fours and couples of sixes during his 23-ball cameo.
Pretty much like yesterday, four dismissals out of the six were edges to wicketkeeper Upendra Yadav, who earlier in the day made an unbeaten 67 to take UP well past 250.
Bad light affected play for the second day in a row.
Brief scores:
UP: 291 all out in 89.5 overs (Mohammad Saif 83, Upendra Yadav 67 not out; Akshdeep Nath 59; Ishant Sharma 3/38, Navdeep Saini 3/47).
Delhi: 228/6 in 75 overs (Gautam Gambhir 86, Dhruv Shorey batting 65; Saurabh Kumar 3/74).
Other brief scores of Group A matches:
Hyderabad 1st innings: 474/9 decl in 148.4 overs (Ambati Rayudu 112, BP Sandeep 82; Manish Rao 3/76, Karan Thakur 3/96).
Railways 1st innings: 35/1 in 13 overs
In Pune:
Maharashtra 1st innings: 245 all out
Karnataka 1st innings: 461/2 in 125 overs (Mayank Agarwal 219 batting, Ravikumar Samarth 129).
Disclaimer: No Business Standard Journalist was involved in creation of this content