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.
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.
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Sanju Samson (20), Karun Nair (32) and Sam Billings (24) were all guilty of throwing away their wickets after good starts.
Pawan Negi contributed unbeaten 19 off 12, getting 13 runs of last over bowled by paceman Ashoke Dinda (1/34).
(REOPENS DEL 84)
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.
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.
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.
Earlier, Dinda was consistent in hitting the right areas from the start and bowled at a decent pace to contain the home openers. He bowled five dot balls to young Riashabh Pant (2) and the pressure got the better of the young batsman, who missed the line while trying to whack one out and was bowled in the paceman's second over.
Dinda, who was very impressive in his first two overs, conceded two boundaries in his third to Nair, who drove the first ball to cover region fluently and then relished a waist height full toss which he dispatched to fine leg boundary.
Daredevils were going at a decent pace but Samson fell to a soft dismissal, ending his 35-run partnership with Nair, when he chipped one straight to R Ashwin at mid-wicket. That was the last ball of power-play with the hosts sitting pretty at 48 for two.
Billings, who had made an impression on his debut at this very ground against Kolkata Knight Riders, joined his captain Duminy at the crease.
The England batsman brought the crowd to its feet when he smashed R Ashwin for two consecutive sixes in the 13th over. Duminy then brought up the team hundred with a couple in the last ball of that over.
Bhatia returned to complete his quota and dismissed Billings, who attempted a switch hit and found the fielder near boundary ropes. Bhatia finished with excellent figures of 4-022-2.