The unfortunate Figueirense keeper was at fault for all three Palmeiras goals, starting in the seventh minute of Saturday night's game when he allowed Thiago Heleno's header to slip though his legs and into the net.
Two minutes later, Wilson mistimed his attempt to clear Marcos Assuncao's cross, allowing Henrique to head into the goal.
Aloisio pulled one back for the hosts in the 64th minute but three minutes later, Wilson failed to hold another cross and collided with a team mate as former Roma and Real Betis midfielder Marcos Assuncao tapped the ball into the empty net.
Both teams remained in the Brazilian championship relegation zone. Former South American champions Palmeiras are 18th with 23 points, one place and point ahead of their opponents.
Kleina replaced former Brazil and Portugal coach Luiz Felipe Scolari who quit earlier this month after a series of poor results in the competition.
Leaders Fluminense beat Nautico 2-1, helped by former Lyon striker Fred's 12th goal of the competition. They have 56 points 26 games, five more than Ronaldinho's Atletico Mineiro who have played two games less.
Santos, missing suspended striker Neymar, lost 3-1 to Portuguesa.