In reply to NSW's 310 in Sunday's clash at Cricket Central in Sydney, Victoria reached the victory target with a whopping 74 balls to spare.
Kellaway (117 not out off 101 balls) and Handscomb (91no off 52 balls) led the way, combining for an unbeaten 145-run stand on the way to the bonus-point win.
Victoria will now meet South Australia in the March 1 final, with the ladder-leading Redbacks earning hosting rights.
Victoria started the last round of the season in fourth spot on the ladder.
But third-placed Queensland's shock loss to last-placed WA opened the door for Victoria to leapfrog NSW, who started the round in second.
Things were going swimmingly for the Vics when NSW crashed to 6-181 following the departure of Jack Edwards in the 34th over.
It looked set to become 7-181 next ball - only for Handscomb to drop an absolute sitter at square leg.
Chris Green was facing his first ball when he skied Sam Elliott to Handscomb, who bobbled the simplest of catches.
Green went on to make 57 off 47 balls among a 117-run partnership with Lachlan Shaw (80 off 67), helping lift NSW above 300.
A 106-run opening stand between Kellaway and Harry Dixon (57 off 37 balls) set up Victoria's run chase, with Handscomb joining in on the fun once Marcus Harris departed for 37.
Handscomb received a life on eight when wicketkeeper Josh Philippe grassed a tough one-handed diving attempt.Â
He was still on eight when he survived a tight lbw shout.
Handscomb made the most of the reprieves to produce a vital knock, cracking 12 fours and two sixes in a raw display of power and finesse.
Kellaway was equally impressive, with his 13 fours and three sixes lifting him to a maiden One-Day Cup century.
It marked a disappointing end to the season for NSW, who entered their last match of the regular season in second spot but knowing a loss would cost them a berth in the final.
Blues opener Sam Konstas made a scratchy 18 off 38 balls before charging down the wicket to Todd Murphy (3-46) and being stumped.
Murphy sent Moises Henriques (15) and Oliver Davies (24 off 20 balls) packing as NSW went from 1-96 to 6-181 despite a defiant knock from Matthew Gilkes (72 off 74 balls).
Handscomb's dropped catch was an important turning point, with Shaw and Green taking control of the innings from that point.
But Victoria made light work of the big chase, going at more than eight runs an over to not only snare the win, but also the bonus point.
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