In the 14th minute Myer Bevan scored his first goal for his country, in just his second international match, showing his poacher's instinct to be first to a rebound inside the six yard box.
Seven minutes later the All Whites' lead doubled, after a speculative Kosta Barbarouses shot looped off Nelson Sale's head into the Solomons Islands net.
The result means the All Whites will face the fifth placed South American side in a two legged playoff in November for a golden ticket to the 2018 World Cup in Russia.
The first match will be in Wellington on November 10 or November 11, with the away leg on the South American continent set five days later.
The All Whites' performance on Tuesday in Honiara continued a trend under coach Anthony Hudson, where they have found a way to get the job done in tough conditions.
It wasn't always polished, but it was professional and efficient, especially considering the raft of personnel changes made since the first leg.
The All Whites paced themselves well in the stifling heat and humidity, with a deliberate strategy to slow the game down. It was a physical battle, with the home side guilty of some rash challenges.
As expected, Hudson's team for this match had a vastly different look about it.
There were significant changes to the starting XI, with Andrew Durante and Tom Doyle coming into defensive back three, Moses Dyer making a rare start and Themi Tzimpoulos used in Michael McGlinchey's defensive midfield position, with the Wellington Phoenix stalwart rested after picking up a yellow card last Friday.
Tzimpoulos looked comfortable further forward, with good positioning and some neat touches in possession and Doyle was solid alongside Durante.
The 20-year Bevan gave an energetic display, and his goal was all about desire, after Storm Roux's shot hit the post and created havoc in the Solomons Island's penalty area. However Bevan blotted his copybook with a needless yellow card in the second half, which could have ramifications for the matches in November.
The All Whites won't be completely satisfied with their defensive effort, especially conceding two more penalties, after one last Friday in Albany. There was no debate about the first, after Lea'alafa was too quick for a lunging Durante midway through the first half and the Auckland City midfielder dispatched his spot kick with aplomb. But the second penalty was hard to understand, with a referee finding a foul after a Solomon Islands attacker appeared to go down rather easily between Durante and Sam Brotherton.
Goal keeper Stefan Marinovic prevented further damage to the scoreboard with a couple of fine saves, as the defence at times failed to close down advancing Solomons attackers.
New Zealand 2 (M Bevan, own goal)
Solomon Islands 2 (M Lea'alafa pen, H Fa'arado pen)
Halftime: 2-1
