After being bowled out for 226 in their first innings that gave Delhi a substantial lead, the visitors were two without loss at the close of play on the third day.
Ahead of a gruelling final day's play at the Feroz Shah Kotla, Tamil Nadu trailed Delhi by 327 runs with all their wickets intact.
Resuming on 31 for one in response to the hosts' first-innings total of 555, Tamil Nadu lost wickets at regular intervals to lend Delhi the upper hand.
Awana finished with figures of four for 53 from his 19 overs, while his other pace colleague, Pavan Suyal, picked up three wickets for 76 runs.
The start was disastrous for Tamil Nadu as they lost Baba Aparajith (25) on the first ball of the morning when his extravagant cut shot was caught at second slip off Suyal.
Awana had the other overnight batsman K B Arun Karthik (8) trapped in front with an incoming ball to leave the visitors reeling at 46 for three.
Tamil Nadu's middle-order mainstay Subramaniam Badrinath (19), too, did not last long as he was caught behind by Punit Bisht off Narwal.
With 327 still needed to make the hosts bat again, Tamil Nadu's batting looked in complete disarray with the Delhi seamers, led by Awana, exploiting the conditions by bowling an accurate line and length.
Tamil Nadu went to lunch at 110 for four with Dinesh Karthik (75) and left-hander R Prasanna (58), the last specialist batting pair, still around.
Halfway through the second session of play, the visitors were at 158 for four in 53 overs with Karthik and Prasanna continuing with the repair job. More
