Delhi made optimum use of fielding first by dismissing Saurashtra in 33.2 overs before Rishabh Pant smashed 40 off 28 balls to help his team reach 194 for eight at close of play.
The other significant contribution from the bat came from Manan Sharma, who made 33 off 65 balls.
However, Delhi's high-profile top-order failed to fire again with Shikhar Dhawan (16), captain Gautam Gambhir (16) and Unmukt Chand (10) falling cheaply to leave the team at 57 for four.
Gambhir, who was released from India's squad for the ongoing England series, too did not last long while Chand suffered his fourth failure in as many innings.
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After shining with the ball, Sangwan shone with the bat as well. Batting at number nine, Sangwan struck an unbeaten 39 off 60 balls to extend the lead further.
The left-hand pacer was impressive with the ball alongside Narwal, ripping through the Saurashtra batting. Only Only Prerak Mankad and Snell Patel showed some resistance with the bat scoring 33 and 26 respectively for Saurashtra.
Delhi 194/8 in 43 overs (Sangwan 39 batting, Pant 40; Kushang Patel 4/59).
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