Resuming at overnight 248 for 5, Delhi added another 105 runs from 27.2 overs at the cost of losing five wickets as light rain and bad light affected the day's play at the Feroze Shah Kotla here.
Delhi lost two quick wickets in the form of Puneet Bisht (3) and Shivam Sharma (0) before Manhas also fell as eighth batsmen dismissed at team total of 286.
Manhas, who was on 55 overnight, added 29 more runs today, hitting seven fours and a six in his 205-ball innings of nearly five hours.
Saini hit six boundaries and a six in his run-a-ball unconquered innings of 54 minutes.
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For Odisha, pacer Basant Mohanty took four wickets today to end with innings figures of 5/76.
In reply, Odisha were 25 for one in their first innings with opener Girjia Rout and Govinda Podder batting on 14 and one respectively at the draw of stumps.
Odisha now trail by 328 runs with nine first innings wickets in hand.
Brief Scores:
Delhi: 353 all out in 111.2 overs (Unmukt Chand 117, Mithun Manhas 84, Navdeep Saini 42 not out; Basant Mohanty 5/76).
Odisha: 25 for 1 in 7 overs.