Chasing 136, KKR needed 13 off 25 balls but lost six wickets for seven runs to fall from 123 for one to 130 for seven.
With six needed and facing Ravichandran Ashwin’s hat-trick ball, Tripathi astonishingly cleared the rope to book KKR’s place in today’s final against Chennai Super Kings.
It will be KKR’s first final in seven years, having lifted the trophy in 2012 and 2014.
After Delhi posted a well below-par 135 for five, KKR looked to be in the driving seat with a strong start.
Marcus Stoinis managed 18 off 23 and big-hitting Captain Rishabh Pant scored just six. Shreyas Iyer (30 off 27) hit 15 off the final over, though, to ensure Delhi at least posted a competitive total.
Delhi Capitals: 135/5 in 20 overs (Dhawan 36, Chakravarthy 2/26)
Kolkata Knight Riders: 136/7 in 19.5 overs (Iyer 55, Gill 46, Rabada 2/23, Ashwin 2/27) (Agencies)