Sarangi was unbeaten on 76 while Behera made 62 at the top to take the hosts closer to Delhi's 311 at the KIIT stadium.
Delhi, resuming the day at 245 for 7, went on to add 66 runs to their total with the help of tail-ender Pulkit Narang (41 not out ).
The home team was in a spot of bother at 40 for two before Behera and Sarangi shared a 77 run stand to steady the ship.
Behera scored at a brisk pace with his innings comprising 12 fours.
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Brief Scores:
Delhi 1st Innings: 311 in 136.1 overs (Milind Kumar 59, Dhruv Shorey 42, Gautam Gambhir 41, Pukit Narang 41 not out; S Pradhan 4/119).
Odisha 195/4 in 67 overs (Natraj Behera 62, Anurag Sarangi 76 batting; Pradeep Sangwan 2/30).