Earlier, Supergiants bowlers did 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.
Khawaja struggled to get his timing early on but played a few good shots after spending some time at the crease. Off-spinner Jayant Yadav (0/25) bowled well for the hosts but the visiting team batsmen managed to survive his spell.
Supergiants openers did not set the field on fire but kept scoring at a steady pace, reaching 59 without loss at the end of eight overs.
Leg-spinner Amit Mishra drew the first blood when he had the Australian stumped with a googly.
Another southpaw batsman came to the crease in the form of burly Saurabh Tiwary as Supergiants were confortably placed at 74 for one after 10 overs.
Tiwary launched Mishra for a six over long-on only in his second ball off the innings. Mishra bowled two no balls in that over but the batsman could not exploit those.
Rahane pulled Brathwaite for a four to bring up his side’s 100 and also inched closer to his half-century with that shot.
Tiwary was sent back by leggie Imran Tahir much to the relief of the hosts camp. Tiwary and Rahane added 45 for the second wicket in five overs.
It brought Pune skipper Mahendra Singh Dhoni to the crease and he began with a monstrous straight hit off Pawan Negi. The shot touched the balcony in the third tier. Supergiants now needed 47 off the last five overs.
It became 37 from three balls as Tahir and Mishra bowled two tight overs. Shami though released the pressure created by the spinners by bowling a wide to boundary ropes. Dhoni then hit the paceman for a four and followed it up with a six.
Tahir again did the job for his side by getting rid of dangerous Dhoni but credit for that wicket should go to Billings, who took a stunner, running to his right and plucking it from the air.