The race for the golden eagle was blown wide open as Kubacki jumped 139 and 144m to amass 282.1 points.
Halvor Egner Granerud led after the first round with a jump of 137m, but the pressure was on in jump two as he went right after Kubacki's world-beater and his 136m effort wasn't enough to overtake the leader, leaving him in second place on 274.9 points.
Zyla finished in third place on 260.4, just 0.4 ahead of team-mate Stoch a few days after the whole Polish team looked like missing much of the tournament following a positive coronavirus test in Oberstdorf which proved out to be false.
Kubacki's record-breaking jump eclipsed the previous record of 143.5m set 12 months ago by Marius Lindvik.
Norwegian Lindvik was unable to defend his 'GaPa' title due to toothache which has worsened since Christmas.
"It was a really great competition for me, really good jumping. I was only one point behind the leader after the first round - it was also a really great jump, maybe a bit different wind conditions," winner Kubacki told FIS afterwards.
"The second jump felt really great in the air, maybe a bit better wind conditions, good landing... hill record, that's really amazing."
Next up is the Innsbruck Bergisel Ski Jump as the Four Hills Tournament heads to Austria for the final two legs.
Kubacki has happy memories from last season as he took top spot last year before going on to win the Four Hills tournament crown and lift the golden eagle.
Meanwhile, Karl Geiger was unable to repeat his heroics from Oberstdorf where he made a stunning return from coronavirus to win the Four Hills opener.
A 131m first jump left him down in 14th place, but a fine second leap of 138m lifted him to fifth to keep him in contention for the Four Hills crown.
Granerud leads Geiger after two events by four points with Stoch a further 2.7 points as the Pole seeks a third tournament triumph.
Eisenbichler hasn't found that X Factor since winning the first two World Cup competitions of the season.
This was Kobayashi's best showing in some time as he tries to rediscover the form which saw him complete a rare Four Hills Grand Slam in 2019, making him just the second non-European tournament victor after compatriot Funaki Kazuyoshi.
Robert Johansson finished down in 18th as Norway's 'Flying Moustache' continues to struggle.
Slovenian jumper Anze Lanisek will also feel disappointed after topping the scoresheets in qualification, the 24-year-old ending up only 12th in the competition proper.
Coronavirus at the Four Hills Tournament
The competition has not been Covid-19 free, but has dealt with positive results efficiently enough to allow the tournament to continue.
Athletes are regularly tested and a positive test of a Russian athlete on Wednesday led to some of team going into isolation according to Dr Martin Fleckenstein, head of the the New Year's Jumping Medical Committee.
Dr Fleckenstein told the FIS website, "The athlete in question is in quarantine. In addition, three other members of the Russian ski jumping team, including another athlete, have been classified as category I contacts and have also been quarantined."