Knowing a victory at Go Media Stadium on Sunday would all but lock up a home qualifying final, the Kiwis were handed a pre-game setback, with halfback Te Maire Martin held back on his return from a hamstring niggle.
It meant 21-year-old debutant Cleary was thrust into the fray alongside two-game five-eighth Luke Hanson.
But the club's newest halves pairing - buoyed by having Cleary's brother Nathan and father Ivan in the stands - showed impressive maturity as the Warriors held off the determined Newcastle.
Cleary (three try assists, 220 kicking metres) was given a leg-up after Knights prop Jacob Saifiti was sent off in the 12th minute for a reckless high tackle on club debutant Luke Laulilii, who failed his HIA.
Although back-rower Jermaine McEwen stormed over for the visitors minutes later, the home side then piled on eight tries to three to keep alive their hopes of securing a first minor premiership since 2002.
"I think we had 11 players under the age of 23, and (we) held our nerve," coach Andrew Webster said.
"He (Cleary) came up with a couple of big plays ... he got our night going.
"I knew that he had that in him ... not being scared of certainly getting roughed up."
The Warriors (40 points, +309) will need to beat Manly on Saturday and hope second-placed Penrith (40 points, +308) lose, or win by a smaller margin than them to snatch top spot.
Adding more pain to their defeat, Newcastle back-rower Francis Manuleleua dislocated his shoulder and will go for scans.
The Knights (14-10) will also rue what might have been if they had 13 players, as they now must rely on the Sydney Roosters beating South Sydney on Friday to lock up a home final.
"This time of year, every team wants their best players on the field, so it would be nice if the send-off was enough," coach Justin Holbrook said after admitting Saifiti's tackle was awkward-looking.
"We wanted to win, so it secured our home final. To be honest, I'm not fussed if we play home or away."
Newcastle opened the scoring when Fletcher Hunt soared across the line, before Manuleleua crashed over.
But the visitors' afternoon soured after Saifiti's send-off and McEwen's try.
In-form second-rower Jacob Laban, hooker Wayde Egan, lock Erin Clark and substitute Demitric Vaimauga all made light work of their opponents' frazzled defence, but Hunt crossed for his second to help the Knights trail 22-20 at the break.
Centres Ali Leiataua and Adam Pompey put the Warriors in the box seat, but winger Greg Marzhew snared a quick double to close the deficit to two points.
However, winger Alofiana Khan-Pereira and Laban surged over to complete the roller-coaster win.
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