Falling behind seemed to ignite the Hawke's Bay side and they found a quick response, Matsumoto firing in from a quickly-taken Cory Chettleburgh free kick 10 minutes into the contest.
The hosts then could, and perhaps should, have found themselves 3-1 up just two minutes later but for two excellent saves from Team Wellington goalkeeper Scott Basalaj.
First Basalaj scrambled sideways to smother Tom Biss' goal-bound effort on the end of Andrew Blake's low cross, and then he did even better to palm away Sam Mason-Smith's effort with the Hawke's Bay striker played through on goal.
From there the next 20 minutes saw plenty of industry but few quality scoring chances as both teams battled in the Napier sunshine but as halftime approached a key moment arrived as Martin Canales bundled over Andrew Bevin in the penalty area. Referee John Rowbury pointed to the spot and Jackson did the rest, placing the ball high to Hill's left with the Hawke's Bay 'keeper going the wrong way.
The visitors thought they had increased their lead to 3-1 in first half stoppage time but after Jackson swept home from close range, Rowbury ruled Corrales had run the ball over the by line before getting his cross in.
The second period saw the hosts trying to increase the urgency in possession with Team Wellington less intent on pushing forward and there was little goal-mouth action in the opening 20 minutes of the half but Hawke's Bay were buoyed by the introduction of substitute Paul Ifill.
While the former Wellington Phoenix front man produced several scoring chances but couldn't find his range, Matt Calcott's team were twice denied by Hill, the Hawke's Bay 'keeper making a sensational double save from Mario Barcia and Vieira.
With 11 minutes to go, after an Ifill shot at the other end, Team Wellington broke downfield and Vieira lobbed the ball over a stranded Hill to seal his side's spot in Thursday night's showcase match.
Minor premiership winners Auckland City confirmed their berth in the ASB Premiership Grand Final on Sunday with a 2-1 semi-final victory over Canterbury United at Kiwitea Street.
The hosts were forced to work hard for their win but prolific marksman Ryan De Vries was again the difference, scoring a goal in each half to see off Canterbury United who got on the board late in the first half via Julyan Collett.