Brazil striker Adriano, meanwhile, marked his return from being dropped by scoring the winner for Flamengo in their 1-0 victory over Vasco da Gama in a Carioca championship derby.
Flamengo goalkeeper Bruno also saved a penalty in each half.
Adriano, who missed Flamengo's Libertadores Cup win away to Caracas FC in mid-week, had a quiet game but converted the match-winning penalty seven minutes into the second half.
"I'm the official (penalty) taker and I assumed my responsibility. Sadly, I was unlucky," he told reporters.
It was Adriano's first match since he played for Brazil in a London friendly against Ireland 12 days ago.
Adriano was booked for celebrating his goal by lifting his jersey to reveal a t-shirt with the message "May God forgive those bad people".
Playmaker Diego Souza then put Palmeiras, who are seventh in the Sao Paulo state championship, in front 12 minutes into the second half after keeper Felipe had touched defender Leo's header onto the bar.
Substitute Madson equalised in the 81st but two minutes later Neymar was shown a red card for a foul on Pierre and Robert completed his hat-trick with a shot from outside the box into Felipe's top corner in the final minute.
"Santos may have attacked more but I know it was Palmeiras who created the clearest chances...It was the best game under my command," said Palmeiras coach Antonio Carlos Zago, who took charge in mid-February.
