Opting to bowl after winning the toss, Delhi bowled out Maharashtra for 246 in exactly the last ball of the 50th over at Himachal Pradesh Cricket Stadium.
In reply, Delhi, who lost opener Unmukt Chand (1) cheaply, completed the chase with 35 balls to spare, reaching 250 for two in 44.1 overs.
Dhruv Shorey remained unbeaten on a fine 103 off 121 balls, while opener Hiten Dalal made 87 off 85 balls with 14 boundaries and a six.
Centurion Shorey shared 138 runs for the second wicket with Dalal before adding another 108 runs in the company of Rana.
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Earlier, lower-order batsman Shamshuzama Kazi top-scored for Maharashtra with 59 off 62 balls, helping his side inch closer to 250.
Among Delhi bowlers, left-arm seamer Pradeep Sangwan was the most successful, returning impressive figures of 5/41 in nine overs.
Pacer Ishant Sharma, who was part of the India squad for the Tests in South Africa, led the side and went wicketless while conceding 64 runs in nine overs.
For UP, young Akshdeep Nath slammed an unbeaten 103 off only 72 balls, hitting 11 fours and two sixes.
In another match of the same group, hosts Himachal Pradesh overcame Kerala by one wicket at Nadaun.