Both sides had chances in a contest that only came to life after the interval, but it was City that proved more clinical in front of goal as Kennedy and Novillo finished off two swift counter attacks to upset Phoenix at home.
It sets up the first derby finals match in A-League history as Premiers' Plate holder Victory meets City on Friday night for a place in the grand final.
Phoenix will be disappointed with how a season that promised so much petered out in the final stages, as well as the relative low turnout of 10,171 at Westpac Stadium.
Wellington made just one change from the side that lost to Sydney FC in the final round with Glen Moss returning in goal, while City had Paulo Retre come in for the suspended Kew Jaliens at the back.
Phoenix was full of attacking intent from kick-off with Nathan Burns in determined mood. The Socceroos striker hit a long range shot that whistled past the City post in the opening three minutes.
As the half wore on City began to threaten in attack. On 25 minutes the visitor played a short corner and Novillo struck a firm shot from the edge of the box that had to be cleared off the line before Moss gathered.
Minutes later Phoenix winger Michael McGlinchey curled in a superb free-kick from just outside the area that hit the crossbar.
Wellington made a bright to the second period. Roly Bonevacia played a brilliant ball through to Burns who burst into the area and fired across goal, but it was too strong for the incoming McGlinchey.
At the other end City was still causing problems to the host's defence. Approaching the hour Jonatan Germano sent an inviting cross into the box for Kennedy. The towering striker stuck out a boot and his effort went just wide.
In a repeat of the same move a minute later with the same protagonists, Kennedy this time glanced a header past the post.
On 61 minutes Melbourne finally made the breakthrough. After a swift counter attack Novillo jinked his way into the area and while he lost possession, the ball fell into the path of Aaron Mooy.
Mooy struck it first time across goal and Kennedy was perfectly placed on the six-yard box to turn it beyond Moss and give City a 1-0 lead.
Phoenix had an excellent chance to hit back five minutes later. A deflected Roy Krishna shot fell dropped perfectly for Burns who was free right in front of goal. Yet the striker's header lacked conviction and was saved by Tando Velaphi.
On 72 minutes the host was undone again by a swift counter attack. Once more the ball found its way to Novillo on the edge of the box. He cut inside with his shot taking a deflection then hitting the post and bouncing off Moss into goal to double City's lead.
Wellington pushed forward in the dying stages yet it barely troubled Velaphi as City held on for a 2-0 win that sealed its place in the semi-final with Victory.
For City, the place in the last four is a remarkable turnaround from last season when it finished bottom of the league.
Kennedy, one of many new faces in the City side, said the team deserved credit for turning around terrible late season form.
"After a few tough weeks, we dug deep," he told Fox Sports.
"We'll be ready for next week."
Van 't Schip knows his side enters the contest as the unfancied side of Melbourne but that is fine by him.
"They've had a great season, but this is a totally different game. It's a final game, everything can change in one moment," he said.
"The pressure is on them.
"We are happy to be there, we'll give it a go and if we are that strong as we were today I'm sure we'll make it very difficult."