Supergiants' bowlers had earlier done a good job, especially in the middle overs, to restrict the in-form Delhi Daredevils to 162 for seven after inviting the hosts to bat.
Chasing a modest total on a good track, Supergiants crossed the line easily in 19.1 overs with Rahane carrying his bat. The opener scored unbeaten 63 off 48 balls while skipper Mahendra Singh Dhoni played a fiery 27 off 20 balls.
Supergiants remained at number six in the points table but got a crucial win under their belt, having struggled to find their feet in their debut season after losing some key players to injuries.
It was only third win for the Pune outfit after losing six matches.
JP Duminy, who led the Daredevils in place of Zaheer Khan, was top-scorer for the hosts with a 34-run knock, which came off 32 balls with just one shot to the fence.
Sanju Samson (20), Karun Nair (32) and Sam Billings (24) were all guilty of throwing away their wickets after good starts. The Supergiants stifled the Daredevils innings with excellent bowling from Rajat Bhatia (2/22) and R Ashwin (0/34) in the middle overs.
Had it not been for some powerful hits by Carlos Barthwaite (20 off 8), Daredevils would have struggled to find momentum. Pawan Negi contributed unbeaten 19 off 12, getting 13 runs of last over bowled by paceman Ashoke Dinda (1/34).
Supergiants openers – Usman Khwaja (30 off 27) and Rahane set up the chase with their 59–run stand. While Khwaja, playing his first IPL match, looked rusty, Rahane was rock solid with his shots.
Last Updated 31, Mar 2018, 6:53 PM IST