The Hurricanes, who won the toss and elected to bat, made a promising start but crumbled under sustained pressure.
England legspinner Adil Rashid (2-16) delivered again to take his wicket tally for the tournament to 14.
The crafty spinner's tight spell peaked with a magnificent wrong'un which ripped through the defence of a hapless Jon Wells.
Hobart skipper Tim Paine (45) set the tone early with an array of aggressive strokes but was run out just short of his half-century.
Hill (32 off 21 balls) pushed the run rate along but the Hurricanes capitulated, with Michael Neser claiming 3-26 and fellow pacemen Greg West (2-24) and Ben Laughlin (2-31) effective.
Strikers coach Jason Gillespie said his batsmen had looked too comfortable at times.
"We certainly feel we nearly made a meal of that," he said.
"With the batting, there was an overriding feeling we left ourselves with too much to do. We needed to shut the game down a lot earlier."
West, who impressed on debut, paid tribute to Lehmann's match-winning heroics.
"I had 100 per cent faith in him when he went out," he said.
"He wasn't nervous, he was good to go.
"There were little lulls in the game which we can work on but we still got the win at the end of the day."
- AAP