Yadav complemented pace bowler Harvinder Singh - who picked up four wickets -- with his seam-up stuff to pick up two wickets and reduce Delhi to 27 for five before the latter were rallied to a modest total of 213 for eight by a valiant knock of 98 by their skipper Ajay Jadeja.
Yadav came to his side's rescue again during the run chase to make a counter-attacking 60 off 65 balls with seven fours and three sixes, putting on a century stand with skipper Sanjay Bangar (55 off 90 balls) in the process, to pave the way for victory after they were left struggling at 68 for three.
Earlier, Delhi were left tottering by Harvinder and Yadav after opting to bat first on winning the toss. They had lost half their side in the 8th over itself before their innings was propped up by the experience of Jadeja.
Jadeja, who was out off the last ball two short of a deserving hundred, hit six fours and three sixes in his 148-ball knock.
Jadeja was given good support by Rajat Bhatia, who made 46 off 74 balls, as the two pulled Delhi out of a deep hole with a stand of 98 for the sixth wicket.
But the final total was not good enough to stop Railways from cruising past it after some initial hiccups.
Railways thus earned a berth in the quarters against last year's runners-up Bengal on April 10.