Lynn was dropped on 13 and 73, while his first boundary sailed just wide of a diving mid-off as he built a relatively sedate innings.
The captain exploded once reaching the milestone, hitting five sixes to finish with 84 off 55 balls.
Lynn took it upon himself to build the inning after the early loss of local talent Max Bryant (34 off 17) stifled their momentum.
Bryant hit two huge sixes as he took to Sydney spinners Ben Manenti and Stephen O'Keefe in a nerveless first two overs.
Jimmy Peirson (23 off 17) joined Lynn with the Heat 5-91 in the 13th over and the paired steered the Heat to 163 before Lynn departed with three balls remaining.
Heat spinner Mujeeb Ur Rahman's second-over maiden put Brisbane in the box seat before Henriques and debutant Justin Avendano rallied.
A rookie error ended Avendano's (30 from 24) enterprising innings, run out by a Cutting direct hit when he failed to ground his bat while completing an easy single.
Henriques soldiered on though, before Silk's crafty knock improved them to 3-2 this season.
The Heat will now travel to Perth for their next clash on Saturday against the Scorchers.