The hosts won the toss and chose to bat first against Delhi, who came into the match with losses from both matches so far this season, and a 11-match losing streak stretching back to last season.
Their stand came to an end in the 14th over when Saha fell short of his half-century, triggering a run of wickets in quick succession, which also saw Sehwag dismissed for 47.
Delhi's reply was aided by some sloppy bowling in the opening couple of overs, allowing Sumeet Agarwal to get on the offensive, smashing the ball to the boundary.
Shreyas Iyer took a little while to get off the mark, and found himself heading back to the pavilion just two deliveries after finally finding a gap.
Agarwal worked well with Yuvraj Singh at the crease though, soon reaching his 50 with a six in the 15th over, leaving Delhi needing 48 off the final five.
Yuvraj soon passed the half-century mark too as the visitors closed in on their target, but both batsman were dismissed by Anureet Singh in the penultimate over, leaving the victory in doubt.
They needed just three off the final six deliveries though, and Mathews tied the scores before hitting a boundary to seal the win with one ball to spare.