Peirson (57no off 43 balls) had a willing ally on this occasion in English import Sam Hain (73no off 41), who bludgeoned the Stars attack.
The duo came together at 4-55 in the seventh over to add an unbeaten 133 for the fifth wicket, the highest partnership of the summer for any wicket for the Heat.
They paced their liaison to perfection and took 30 runs off the two overs of the power surge to up the ante.
Peirson, playing his 101st BBL game for the Heat, was pugnacious square of the wicket while Hain unfurled a vast range of shots, including a reverse ramp for six.
It was a rescue mission that could yet prove decisive in ensuring the Heat play finals as they seek a fourth consecutive win.
The Heat can finish as high as third on the ladder if they win their remaining two games, including their final-round encounter with the Hobart Hurricanes in Launceston.
The Stars are last and won't figure in the finals but they started their stint in the field on a mission to ruin the Heat's chances.
England international Luke Wood came out breathing fire and brimstone in a fearsome opening spell.
He blasted out Josh Brown (four) and Marnus Labuschagne (one) in his opening two overs and almost had Matt Renshaw first ball.
Renshaw ran himself out for seven when he took on mid-off Adam Zampa and lost.
Nathan Coulter-Nile cleaned up Usman Khawaja (24) to have the hosts in trouble after captain Khawaja won the toss.
