Sohal made 34 and Dhawan 28 as Deccan Chargers scored 138 for four in 19.2 overs in reply to Pune's 136 for nine.
Deccan, who are already out of contention for the play-offs with one game left, have 10 points from 13 games. Pune have eight points after 12 games and their slim chance of reaching the knockout stage is over.
Earlier, a combined bowling effort from Deccan restricted Pune's total. Amit Mishra, the leg-spinner, Pragyan Ojha, the left-arm spinner, and Daniel Christian, the medium pacer, claimed two wickets each, while Mitchell Marsh, the Australian all-rounder, struck a useful 37 for the losing team.
"We had to win all our three remaining matches in order to qualify," Yuvraj Singh, the Pune captain, said. "Unfortunately nothing went our way and our batting let us down once again."
Deccan always had the chase in control after the opening stand lasting 8.1 overs. Sohal struck two sixes and two fours off 28 balls, while Dhawan hit four fours off 25 balls before both openers fell in quick succession.
Kumar Sangakkara, their captain, struck 25 off 21 balls and Jean-Paul Duminy, the South Africa batsman, made 23 off 25 to keep the team on track.
Earlier, Mishra bowled a maiden over in which he claimed the wickets of Robin Uthappa and Mithun Manhas. Mishra took an easy return catch to dismiss Uthappa and then bowled Manhas with a lovely googly as Pune slipped to 45 for five.
Pune's total gained some respectability with Marsh batting well at No 8. The 19-year-old son of Geoff Marsh, the Pune coach and former Australia Test batsman, struck three sixes and a four off 28 deliveries to repair some of the damage inflicted by Deccan's bowling combinations.
Yuvraj and Manish Pandey, the opening batsman, chipped in with 23 apiece but the team failed to put on any useful partnerships.
For Deccan, Christian struck at crucial junctures to account for Sourav Ganguly, the former India captain, and Yuvraj, while Ojha dismissed well-set batsmen Pandey and Marsh.
Royal Challengers Bangalore, the table-toppers, and Kings XI Punjab clash in the northern hill city of Dharamsala tonight.
Glad to leave the IPL on a winning note, Sangakkara summed up the Chargers' season when he said there was much to be done to improve.
"We have to do a lot of work, be more athletic, fielding will be a key for us. Batting and bowling, skill wise, we are alright," the former Sri Lanka captain said, before adding that he was looking forward to playing Test cricket again.