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 clapped back as the supporters applauded him.
He is due to start treatment for the illness on Monday.
Chelsea won the match 4-2 with two late goals after Villa came from behind to level the score at 2-2.
Villa manager Alex McLeish agreed it was an emotional afternoon at Villa Park, telling Sky Sports News: "Its a measure of how popular the guy is.
"Not only at this club, but his former club Celtic and the Bulgarian nation will be rooting for him and in the whole of football - everyone has respect for 'Stan'.
"We are right behind him and his recovery and he has taken his first couple of steps in the last couple of days.
"He is a determined guy and he will fight it and beat it and that is typical, I would expect that from him."
Bulgarian team-mate Martin Petrov, no relation, wore a message of support when his Bolton Wanderers team played at Wolverhampton Wanderers and said he was determined to score for his old friend.
He did just that - with a penalty in Bolton's 3-2 win at Wolves.
Martin Petrov told Sky Sports News: "I lived with him for two years at the start of our careers in Bulgaria. This morning I told my gaffer [Bolton manager Owen Coyle], that I was playing for him, so we win, and I score a goal."
Chelsea's players wore T-shirts during their warm-up with Stiliyan'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's 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 halftime substitution.
"I lost my energy early in the second half and it wa
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