Kohli, who got two reprieves during his sensational knock, along with with A B de Villiers put on 94 runs off just 40 balls for the fourth wicket to power RCB to 183 for four at the Feroz Shah Kotla.
Left-arm pacer Unadkat then picked up five wickets for 25 runs to help RCB restrict Delhi to 179 for six.
Both Jaywardene and Sehwag fell to Unadkat.
While Jayawardene (19 off 13) played on to his stumps in the fourth over, Sehwag (18 off 10) was foxed by a slower delivery as he spooned one straight to Cheteshwar Pujara at mid-on.
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To add to Delhi's woes, stand-in skipper David Warner too failed to make an impact. He was bowled by a quicker delivery from Moises Henriques.
RCB skipper Kohli's decision to introduce Jamaluddin Syed Mohhamd backfired as the left-arm spinner went for four boundaries -- one by Unmukt Chand and three by Ben Rohrer - to concede 20 runs off the ninth over.
Just when the duo of Chand and Rohrer (32 off 27) were looking dangerous, the later departed inside edging a R Vinay Kumar delivery on to his stumps. The fourth wicket partnership of Chand and Rohrer yielded 58 runs off 44 balls.
The asking rate took a toll on Chand too as he also departed soon, caught by Vinay Kumar off Unadkat. He scored 41 off 35 balls with the help of four fours and a six.