A Ricardo Clark diving header opened the scoring for the two-time defending MLS champ but soon enough Bare and Gamba riddled the Dynamo's central defense.
Another Brazilian, Lucas, and Masato Yamazaki each notched a goal as Osaka lived up to the promises of Coach Akira Nishino, who before the tournament began said his team wanted to display its attacking power.
Following the rout, he said, "I am very pleased with how we used an aggressive style and we showed that we have very strong condition."
Osaka had dominated the Galaxy in its first match but missed numerous chances after Bare scored early and won by just the single goal.
Houston had arrived in Hawaii somewhat short on condition, having trained for about three weeks, and banged up as well. Midfielder Brian Mullan didn't play in either match and Coach Dominic Kinnear sent out a three-man back line in the opener against Sydney rather than his preferred quartet because of injuries to several defenders.
Local product Brian Ching set up two of the goals in a 3-0 Dynamo defeat of Sydney in the semifinal, but he and his attacking mates seldom got into a rhythm against Gamba despite taking that early lead. At the other end, soft pressure in midfield and confusion between defenders Pat Ianni and Bobby Boswell left keeper Pat Onstad utterly marooned on several goals.
In the third-place match, David Beckham helped set up both goals in a 2-1 Galaxy defeat of Sydney FC, offering Los Angeles some payback for a 5-3 defeat inflicted by Sydney when the teams played a friendly in November.
After playing horrendously in the first half against Gamba and improving somewhat after the interval, Los Angeles pushed forward from the kickoff and stunned Sydney in the third minute when Ely Allen crashed home a shot from a Beckham cross.
Brendan Renaud tied the match with a blistering shot into the top corner late in the first half, but Los Angeles regained the lead before the break when Josh Tudela knocked home a Beckham cross that Sydney keeper Ivan Necevski had bobbled.
The attendance of 23,087 in the 50,000-capacity stadium for the PPC final and third-place game is a record for a pro soccer game in the Aloha State but still left more seats empty than occupied. Still, Gamba's sparkling play surely pleased the fans as well as the tournament's sponsors, many of them based in Japan.
Carlos Ruiz, who had aggravated a knee injury early in the month, and Landon Donovan, also bothered by a knee problem, sat out both Galaxy games rather than risk further injury on the Aloha Stadium artificial turf.
"This is a good start to our preseason," said Galaxy coach Ruud Gullit. "We are making good progress and I am pleased with how things have gone in Hawaii."
Said Sydney head coach John Kosmina, whose team had been eliminated in the A-League semifinals in early February after finishing the regular season in third place: "It has been very tough for us out here but we have gained from the experience. It has been a long year for us and the boys will be pleased to get a bit of rest in."
There's no rest for the Galaxy. Their cross-Pacific tour heads further east for games in Seoul and Shanghai next week. Houston returns home and begins play in the Texas Pro Soccer Festival March 5.