Head (23) never quite got going, eventually top-edging a catch to Badree off leg-spinner Mitch Swepson, who bowled a fine 18th over.
Kieron Pollard (one) and Jake Lehmann (first ball duck) had their castles disturbed, the home side fading at the death, finishing on 6-196.
Mark Steketee was the pick of the bowlers with 3-32 while Ben Cutting grabbed 2-46. Earlier, Alex Ross cracked 64 against his old side to build on the foundation laid by Heat keeper Jimmy Peirson (46) and McCullum who smashed 90 in the first eight overs.
Former Black Caps master blaster McCullum should have been run out on 35 and was grassed by Kane Richardson before Pollard (2-27) snared Peirson and McCullum off successive deliveries.
Pollard further shifted the momentum after his high-leaping catch at deep midwicket sent dangerman Chris Lynn (29) packing.
The scoring rate temporarily slowed before Ross took charge.
Ross paid tribute to Badree's match-turning 14th-over maiden, on the back of Dunk's dismissal.
"In hindsight it was a pivotal over - it turned the game," Ross said.
"Then Cutts and Stek at the end, under pressure were awesome.
"If we can do that all season we'll be a very tough team to beat."
"When you're chasing over 200, everything needs to go right," Dunk said.
"Between us (Dunk and Weatherald), we gave ourselves a chance.
"Full credit to the Heat, they bowled really good death bowling and we couldn't quite get the job done."
- AAP