Chasing a mammoth 209, the left-right combo of Pant (97) and Samson (61) plundered the Gujarat bowlers all over the park to raise a 143-run stand of mere 63 balls to overhaul the target with 15 balls to spare.
With this win, sixth-placed Delhi kept their hopes of qualifying for the play-offs while Gujarat, languishing in the penultimate spot, are already out of the race.
It was a steady start for Delhi as Sanju Samson and skipper Karun Nair (12) scored 24 runs in three overs but on the fifth delivery of the third over, Nair was sent back to the pavilion by medium pacer Pradeep Sangwan.
Trying to pull a short delivery Nair found an edge that perfectly landed in wicketkeeper Dinesh Karthik gloves.
The fall of wicket brought in Pant, who along with Samson created havoc among Gujarat's bowlers.
Both batsmen added 143 runs for second wicket in just 10.3 overs before Samson was dismissed by Ravindra Jadeja in the 14th over.
Samson's 31-ball innings comprised seven sixes.
Unperturbed by the fall of Samson's wicket, Pant continued to beat the leather but with three runs short of his century, Pant was sent packing by Basil Thampi.
Pant, who slammed six boundaries and nine sixes in his 43 ball innings, got a nick and wicketkeeper Karthik made no mistake to grab the ball.
With pace of the game perfectly set by the former batsmen, middle-order batsmen Shreyas Iyer (14) and Corey Anderson (18) then completed the proceeding comfortably without any hiccups.
For Gujarat, Sangwan, Thampi and Jadeja took one wicket each.
Earlier, put in to bat, crafty knocks by skipper Suresh Raina and Dinesh Karthik helped Gujarat post a challenging 208/7 against Delhi.
Raina (77) and Karthik (65) came to the crease when the visitors were reeling at 10/2 in the second over. But sensible innings from the duo helped Gujarat to get out of troubled waters.
Gujarat got off to a poor start as they lost swash-buckling openers Dwayne Smith (9) and Brendon McCullum (1) in the second over of the innings.
McCullum was the first one to depart. The New Zealand batsman got an outside edge off pacer Kagiso Rabada and Rishabh Pant then completed the rest of the formality by taking a superb catch.
Off the very next ball, Shabaz Nadeem did a brilliant job in the field, coming up with an accurate direct throw to dismiss Smith.
With the visitors reeling at 10/2, incoming batsmen Raina and Karthik then stepped up to tackle the situation and thrashed the Delhi bowlers all around the park.
The duo forged a brilliant 133-run partnership for the third wicket before Raina was run out by Rabada in the 14th over. A slight miscommunication between Karthik and Raina helped Delhi break the partnership.
In-form batsman Aaron Finch (27) then joined Karthik and both batsmen tried to rev up the innings. But soon Karthik was sent back to the pavilion by pacer Pat Cummins.
While trying to play over mid-off, Karthik mistimed the ball and Correy Anderson took a stunning one-handed catch to dismiss the Delhi wicketkeeper.
With the score at 158/4 in 15 overs, middle-order batsman Ishan Kishan (4), who joined Finch, failed to click as he was also dismissed by Cummins in the 18th over.
With two overs remaining, Finch played some good strokes and he was also supported by Ravindra Jadeja (18) but just when things seemed good for the visitors, Finch was caught at fine leg. Wicketkeeper Rishabh Pant took a diving catch off Rabada to dismiss the Australian batsman.
James Faulkner was also dismissed in the last over by Corey Anderson. But then Jadeja finished off the things in style by slamming two huge sixes in the last two deliveries of the final over.
For Delhi, pacers Rabada and Cummins scalped two wickets each.