Palmer whipped through the concrete bowl in an opening run packed with tricks to grab the lead with a score of 93.11, which would ultimately prove enough as Schaar was unable to stay attached to his board in his final run.
Brazil's Augusto Akio edged countryman Pedro Barros to take bronze.
With the title secured before his final run, Palmer took a victory lap in front of the boisterous crowd, which included skateboarding legend Tony Hawk and rapper Snoop Dogg.
Barros and American Tate Carew skated out to meet Palmer on the jump box in the middle of the bowl and lifted the 21-year-old up on their shoulders in a great show of sportsmanship.
Three years ago, Palmer came out of nowhere to dominate the inaugural park competition in Tokyo but was a favourite coming into Wednesday's final.
He won the preliminaries earlier in the day with his blistering speed, huge air and complete control and did not let up in the final at La Concorde.
Palmer's triumph followed 14-year-old Australian Arisa Trew winning the women's park event on Tuesday.