After restricting the hosts to 213 for nine in 50 overs, Pakistan romped home with 7.2 overs to spare with Misbah-ul Haq (39) and Yaseer Hameed (33 not out) contributing bulk of the runs.
Amit Bhandari was the pick of the Delhi bowlers claiming one for 25 in his seven overs.
Pakistan began their chase in whirlwind fashion and looked in a hurry to wrap up the match. Despite losing Kamran Akmal (5) to Kunal Lal in the first over, the visitors raced to 66 in six overs before Imran Nazir fell to Bhandari.
Butt and Misbah continued the good work before the left-hander retired on 83 which came off 84 balls and included 13 fours and one six. By that time, Pakistan had pocketed the match and it was just a formality which Hameed and Fawad Alam (10 not out) completed as Pakistan read 215 for four in 42.4 overs. Butt was adjudged man of the match.
Earlier, Rajat Bhatia and Shikhar Dhawan hit half-centuries to help Delhi overcome a jittery start after being put in to bat by visiting captain Shoaib Malik.
Delhi slumped to 36 for four inside 13 overs before a 91-run stand between Dhawan and Bhatia arrested the slide. Bhatia’s 75 was a product of his 106-ball stay in the middle and included seven boundaries besides a six off Fawad Alam.
Dhawan’s 52 came off 81 balls and had three fours in it. The left-hander also pulled Shoaib Akhtar over square-leg for his only six.
Delhi ran into trouble soon as stand-in skipper Gautam Gambhir (4) departed as early as in the second over when Umar Gul trapped him plumb in front.
Aakash Chopra (16) and Dhawan struggled to nudge the score along and then Younis Khan dealt a double blow. The Pakistan vice-captain first trapped Chopra and then castled Mithun Manhas for a first-ball duck.
Dhawan did not last long after completing his half-century. A Salman Butt direct throw cut short his stay, leaving the hosts reeling at 137 for five in the 35th over.
Once Dhawan departed, Bhatia started playing his shots even though wickets kept tumbling at the other end.
Mayank Tehlan (7) offered a return catch to Alam while Shahid Afridi scalped Puneet Bisht (2) in his first over.
Bhatia perished when a Sohail Tanvir direct throw caught him short of the crease.