The 34-year-old spin wizard picked up a match haul of 10-172 as South Africa were thrashed by an innings and 153 runs to concede the lead in the two-match series here on Monday.
Muralitharan grabbed 6-131 as the tourists, 587 runs behind on the first innings, were bowled out for 434 in their second knock after lunch on the fifth day at the Sinhalese sports club.
"There is no doubt in my mind that Murali is the greatest spinner ever," said Jayawardene, who was named man of the match for the fourth highest Test score of 374 in Sri Lanka's innings.
"These were difficult conditions to bowl in. It was very hot and humid and the wicket was getting slower, slower and slower as the match progressed.
"Yet Murali bowled 64 overs in the second innings and just kept probing the batsmen. He is so hungry for wickets.
"I am certain he would have been named man of the match if I had not got that big score or the record stand."
Sri Lanka had piled up 756-5 declared in their first innings with Jayawardene sharing a world record partnership of 624 with Kumar Sangakkara (287) for the third wicket.
The batting feast came after South Africa were dismissed for 169, their lowest total against Sri Lanka, on the opening day.
It was the 17th time Muralitharan had claimed 10 or more wickets in a match. He also has 54 hauls of five wickets or more in an innings.
Muralitharan, 34, now has 645 wickets in 107 Tests, second in the all-time list behind Australian Shane Warne's record tally of 685 in 140 matches.
Jayawardene said his team gained enormously from the recent tour of England where they fought back to draw the Test series 1-1 and blanked the hosts 5-0 in the one-dayers.
"That tour gave us the confidence to play better," he said. "We had to make sure we did not go off the boil and needed to stick to our game plan.
"We were very positive in everything we did here. It was a great achievement by the whole team."
South African captain Ashwell Prince, standing in for the injured Graeme Smith, said the low score in the first innings let his team down.
"We had our backs against the wall from the first day," said Prince, the first black cricketer to lead his country.
"In hindsight I would still have batted first on winning the toss even though the wicket got easier on the second and third days.
"As I told the boys, there were too many soft dismissals that caused our downfall and it was always going to be a struggle from there.
"But the guys showed great courage in what were not easy conditions. We batted quite well the second time, which is a great positive to take from the match. We will be better prepared for the second Test."
South African coach Mickey Arthur said touring Sri Lanka was the second most difficult job in cricket after playing in Australia.
"Those are the two toughest tours in the game," he said. "Sri Lanka is such a tough opponent at home."
The tourists, already missing the injured duo of Smith and all-rounder Jacques Kallis, will be reinforced by veteran Shaun Pollock for the second Test starting at the Sara stadium on Friday.
Pollock, South Africa's leading wicket-taker with 394 Test wickets, missed the first Test following the birth of his second daughter.