After failing in the last two matches, Jayawardene scored a solid 82 in a Super Eight match against the West Indies here on Sunday and shared a 183-run stand with Jayasuriya.
"Obviously, Sanath took a lot of pressure off me. He gave me the freedom to play risk-free, straight as much as possible and just occupy the crease," said the Sri Lankan skipper.
Jayasuriya smashed 115 runs off 101 balls for his 25th century to help Sri Lanka post a challenging 303 for five before a capacity crowd at the National Stadium hoping for a home victory.
The West Indies crumbled under the pressure as they were bowled out for 190 in their third straight Super Eight defeat, and now face elimination.
Jayawardene said Jayasuriya had been something special.
"I have seen quite a lot from Sanath, but I would rank this as one of the best. He has done it not just against small teams, in low-key tournaments, but in big tournaments, under pressure. That's what makes him so special."
The Sri Lankan skipper admitted he would have fielded first had he won the toss after a rain-delayed start.
"I lost a difficult toss. That is the difficult part of this tournament. You can't play for the toss. Obviously, if I had won the toss, I would have fielded in those conditions."
He dismissed suggestions of any planning behind West Indian captain Brian Lara's dismissal, a bizzare stump off paceman Chaminda Vaas.
"It was not planned," he said of Lara's dismissal for two. "I don't think that was the only wicket. Brian is in form and he is one of the guys. The only thing we concentrated on was not to give them a big start.
"When we saw Brian batting in front of his crease, we felt we needed to get Kumar (Sangakkara) up. Kumar has worked really hard. If you see him work on his game, it is amazing. I mean, that guy is a workaholic."
Jayawardene said his bowlers kept a tight length and never allowed the hosts an explosive start.
"We managed to get those early wickets and put them under pressure. Obviously Ramnaresh (Sarwan) and Shiv (Chanderpaul) had to bat through to consolidate, but I thought our bowlers did pretty well during that period."
Jayawardene said he was not worried about off-spinner Muttiah Muralitharan losing some runs against the West Indies.
"Murali bowled from a tougher end to a left-hander with shorter boundaries. The wind was also assisting the batsmen, so obviously they would be taking chances. Murali was very happy because one of those shots could have easily got a top-edge and gone up."
The skipper said he was not looking ahead to a final.
"I am not looking too far ahead. If I dream about (lifting the World Cup) it's brilliant but hopefully, not too soon. We just have to concentrate on one game at a time, and that's what I have been telling the guys.
"It's a big tournament, but if you think too far ahead, you won't concentrate on the first post."
Sri Lanka, who lost their first Super Eights match to South Africa by a close margin of one wicket, now have four points and next play England at Antigua on Wednesday.
Their remaining matches are against New Zealand on April 12, Australia on April 16 and Ireland on April 18 -- all in Grenada.