Mohit Sharma and Unmukt Chand scored fine fifties, but the hosts still have the daunting task of scoring 347 more runs for the first innings lead against Baroda, who put up a massive 561, in the Ranji Trophy match at the Ferozshah Kotla, in Delhi, on Monday.
The 20-year-old Mohit scored 71 while the talented Chand 51, as Delhi ended the day on 215 for 3.
At the crease are seasoned pros Mithun Manhas, who looked solid on 41, and Rajat Bhatia, on 9.
Delhi now need 347 more runs on the final day in order to get three points from the game.
Baroda skipper Ambati Rayudu employed defensive fields to cut down on the boundaries, but the Delhi batsmen, especially Mohit, showed a lot of character during his 154-ball innings in which he hit seven fours.
He enjoyed two useful partnerships -- of 87 runs for the second wicket with Unmukt and 78 for the third with Manhas.
The left-hander was impressive against the spinners, and when the field was opened up, he took quick twos to keep the scoreboard moving.
Just when it looked that the youngster would score a maiden first-class century, he was trapped leg before by Firdaush Bhaja.
Unmukt also looked good during his innings, during which he hit some lovely cover drives including one off Bhaja. He hit six fours in all but was bowled by left-arm spinner Bhargav Bhatt failing to read the turning delivery.
A lot was expected of skipper Shikhar Dhawan as he raced to 30 off only 33 balls, with four boundaries, but he mistimed a pull-shot when Murtuza Vahora bowled a bouncer. The ball ballooned up and he was caught in the square leg region.
As of now, Delhi's hopes rest on the shoulders of Mithun Manhas, who has shown good form this season.
Earlier, Baroda batted around 10 overs in the morning to take their score from 525 for 7 to 561 all-out. The two overnight not out batsmen Ketan Panchal and Gagandeep Singh Natt were dismissed for individual scores of 80 and 76 respectively.
National selector Saba Karim was present on all three days and the former India wicketkeeper will certainly be pleased with effort of Parvinder Awana, who took 4 for 104 in 37 overs.
Delhi coach Vijay Dahiya said they would take a call on the chase after lunch tomorrow.
Baroda (1st innings): 561 (Ambat Rayudu 131, Abhimanyu Chauhan 113, Ketan Panchal 80, Gagandeep Singh Natt 76, Parvinder Awana 4-104).
Delhi (1st innings): 215-3 (Mohit Sharma 71, Unmukt Chand 51, Mithun Manhas 41 batting).