Put in to bat at the C.ex Coffs International Stadium, the second-placed Sixers struggled to score quickly on a slow pitch, finishing at 8-141.
Rain interrupted the match with the Heat at 4-80 after 12 overs, two behind where they needed to be under the Duckworth-Lewis-Stern method.
Three overs were lost with Brisbane needing 44 off five overs in a revised target of 124 off 17.
Walter smashed a huge legside six off Tom Curran, the first ball after the break.
He then whacked two fours in the first three balls of the only Power Surge over to lift the Heat to 4-104, three runs above the score required after 14.3 overs, when the second shower ended the game.
Heat moved four points ahead of the Sixers, who were second going into the game.
It was another frustrating night for the Sixers, who had each of their last two games end in a no result due to rain.
Walter and Nathan McSweeney (22 not out off 25) put on 32 for the fifth wicket.
Walter, who took 2-25 off three overs, and McSweeney were earlier involved in the most dramatic moment of the game.
As he raced in the outfield in pursuit of a return catch, Walter and McSweeney chased after the high ball with neither aware they were on a collision course.
The crowd held their breath but the two were lucky to escape with a minor bump, bringing back memories of the sickening collision between Steve Waugh and Jason Gillespie in Sri Lanka in 1999, when the former broke his nose and the latter his leg.
Walter appeared to pull out at the very last moment as McSweeney took the catch.
The Sixers were sloppy in the field early in the Heat innings dropping the dangerous Josh Brown on one and 36.
The latter reprieve gifted to him by Tom Curran came after the hard-hitting opener smashed successive sixes of spinner Todd Murphy later in the over.
The Heat were well placed at 1-60 in the eighth over, but Brown (43 off 31 balls) was then bowled by veteran spinner Stephen O'Keefe and they lost 3-12 before the rain came for the first time.
The Sixers struck six sixes, but just nine fours in their innings.
Left-arm spinner Matt Kuhnemann (2-19 off four overs) bowled particularly well, claiming the first two wickets to fall.
A third wicket stand of 47 between opener Josh Philippe (41 off 36 balls) and Moises Henriques (22 off 22) lifted the Sixers to 2-82 in the 13th over.
But the Sixers lost a wicket in each of the next four overs as their innings declined, losing 6-39.
Jack Edwards (22 off 15) and Ben Dwarshuis (13 not out off 6) added some late substance.
Brisbane's bowling variety, execution and slick fielding were instrumental in keeping the score down.
