The skipper whacked an unbeaten 88 from 55 balls as the Heat secured a valuable 31-run win over Hobart Hurricanes at Bellerive Oval on Friday night.
Lynn whacked 11 fours and three sixes as the rocks-or-diamonds Brisbane posted 3-212, their highest BBL score.
Hobart's chase started promisingly but hit a fatal hurdle when linchpin D'Arcy Short (25) was bowled by the part-time spin of Matt Renshaw in the 11th over.
It is an important bounce back win for the Heat (2-3) after they were all out for 109 chasing 150 against the Perth Scorchers on Wednesday, prompting Lynn to apologise to fans.
Lynn played second fiddle early to young opener Max Bryant, who broke free for the first time this season with 65 from 36 balls.
The pair shared a 95-run stand for the second wicket after English opener Tom Banton (eight) skied Riley Meredith in the second over.
Renshaw chipped in with 30 from 17 late in the innings after the Heat were sent in.
In reply, all of the Hurricanes top five got starts but none could make it past the 20s as they were limited to 9-181.
Hobart's pain was compounded with key allrounder James Faulkner suffering a calf strain which ended his night after just two overs.
Six Brisbane bowlers shared the wickets, with Jack Prestwidge finishing with the best figures of 2-16 from two overs.
Hurricanes' captain Ben McDermott put a scare through the home crowd when he was briefly felled while batting after being struck in the back of the neck from an outfield throw.
Brisbane's score bettered their mark of 4-209 set two matches ago against the Sydney Sixers.
Hobart, last season's ladder leaders after the regular rounds, are 2-3 ahead of a trip to Perth to face the Scorchers on Sunday.