The applause began in the 19th minute at Villa Park - to match Petrov's shirt number - while the 32-year-old Bulgarian international watched the match with his family from the directors' box. He is due to start treatment for the illness on Monday.
Chelsea's players wore t-shirts during their warm-up with Petrov's name and number on the back and with the message: "Our thoughts are with you" on the front. Villa's players had the words "Support Stan" on theirs.
Petrov, capped 105 times for Bulgaria, issued a statement saying he would take inspiration from Bolton Wanderers' midfielder Fabrice Muamba, who is recovering after suffering a cardiac arrest during a match two weeks ago.
"This is a difficult time for my family and myself and I ask people to respect my privacy," Petrov said.
"I saw the picture released yesterday by Fabrice Muamba, my fellow player, and it has inspired me as has all of the support in the past 24 hours.
"For me, football will have to take a back seat for a while, but I'm here to support my team-mates today and I will continue to support them as I know they will support me. Thank you to everyone."
Bulgarian sports daily Tema Sport on Saturday quoted the midfielder as saying: "Football is over, this is the end. I am now beginning to fight for my life and I will fight."
Petrov, a regular for Villa this season, said he had felt a strange headache during the first half of the 3-0 defeat by Arsenal last Saturday and the team doctor had even suggested a half-time substitution.
"I lost my energy early in the second half and it was very unusual for me," Petrov said.
"But this is life, you see we drank a coffee in London a week ago and now we're talking about things like this.
"I'll fight, it's clear and I also would like to thank everyone for the support from all around the world."
An avalanche of support has poured in from all parts of the world for the former CSKA Sofia and Celtic midfielder.
"Let's all pray and believe that Stiliyan Petrov, one of the best football players Bulgaria have ever produced, one of my best and closest friends, will win this battle," Manchester United striker Dimitar Berbatov said on his Facebook account.
"He deserves all your support. Believe," his compatriot added.