Australian Herbert got the job done at the second extra hole, recovering from an errant tee-shot before holing from 12 feet to banish the memory of the travel issues which saw him arrive late into Japan on Wednesday.
Extra holes were required after both players finished the tournament on 15 under par following a thrilling final round in the historic first event to be co-sanctioned by the DP World Tour and Japan Golf Tour Organisation.
After Herbert had narrowly missed his 20-foot birdie try at the 18th, Cockerill played the 72nd hole knowing a birdie would be enough to clinch his first title.
But having found the fairway with a perfect drive, Canadian Cockerill sent his second shot into a greenside bunker - and it looked like Herbert had the advantage.
Cockerill produced a stunning recovery from the sand, though, almost holing his bunker shot before tapping in for a par to force a play-off.
Both men were just off the green after two shots at the first extra hole, with Herbert slightly further back in the fringe.
After Herbert missed his birdie try, Cockerill's effort looked to be heading in before an agonising lip-out extended the contest.
Despite sending his tee-shot into the trees, Herbert managed to knock his second shot onto the green and roll in the putt to claim the title.
Herbert's 67 featured an eagle, three birdies and two bogeys, while third-round leader Cockerill signed for a closing 68 which contained four birdies and two bogeys.
Scotland's Calum Hill was alone in third on 14 under after his closing 65, one shot ahead of countryman Grant Forrest and home favourite Hiroshi Iwata.
Herbert went into the final round one shot off the lead but birdied the first hole to close the gap.
After a spectacular approach into the par-five fifth, the Australian holed his eagle putt from around six feet to jump to 15 under.
Herbert dropped a shot at the eighth but bounced back with a 15-foot birdie putt on the tenth before limiting the damage to a bogey after getting into tree trouble off the tee at the 11th.
He regained the outright lead with a birdie from ten feet at the 12th, which came courtesy of a brilliant approach shot.
Herbert then holed a series of important par putts at the 13th, 14th and 15th before narrowly missing his birdie try on the 16th.
After safely parring the short 17th, Herbert gave himself an outside birdie chance on the 18th but could not convert from 20 feet and had to settle for a place in the two-man play-off.
With both players making par at the first extra hole, Herbert was lucky to avoid serious damage at the second as his tee-shot went towards the trees.
But he got a drop and took full advantage, as he knocked his second shot onto the putting surface and drained the putt to emerge victorious.
The win takes Herbert to fourth on the Race to Dubai Rankings in Partnership with Rolex and earns him a first title since the 2021 Dubai Duty Free Irish Open.
He said: "It's great. Obviously coming on board as an ambassador for ISPS Handa this year, it's great to win an event with them as the title sponsor.
"It's a real honour. And just to be back in Japan and win as well. I've come here so many times and loved it so to get back here and win, it means a lot.
"I think it's cool to be able to win everywhere and have a lot of good memories from all the spots in the world where you have played."
Speaking about the up-and-down that earned him victory at the second play-off hole, Herbert said: "Pretty special. I got pretty lucky over there on the right to get a good lie after we dropped it.
"Nick (caddie Nick Pugh) gave me the number and it was basically perfect. It was exactly what you'd want off that lie.
"So it was good to hit a good shot in there. And then my hand was shaking all over the place just to get the putt started on line, and to have it fall in was pretty cool."
Cockerill got off to a slow start on Sunday, parring the opening three holes before dropping a shot on the par-three fourth to slip out of the lead.
But he bounced back with a birdie at the fifth before four more pars took him to the turn in 35.
The Canadian picked up a shot from around eight feet at the tenth to regain a share of the lead but made his second bogey of the day on the next.
He responded in style, though, birdieing the 12th to return to 14 under before holing his birdie effort from around 18 feet on the 14th to join Herbert at the top of the leaderboard.
Cockerill then produced a sensational par save from 25 feet at the 15th to remain tied at the top before missing the chance to take the outright lead from six feet.
He two-putted for par from long range at the 17th but sent his approach at the 18th into a greenside bunker and had to settle for a tap-in par and a play-off.
With ISPS Handa donating $1,000 for every eagle made during the tournament to the G4D Tour, the tally stands at $40,000.