Sanagakkara led by example in making a fine 111 off 128 balls and also shared a vital 145 runs with his deputy Mahela Jaywardene to pull the team out of early trouble in a Group A match against New Zealand on Friday.
Veteran off-spinner Muttiah Muralitharan then took 4-25 despite a nagging leg injury as the Black Caps were dismissed for 153 to lose by 112 runs.
"That's what our role is all about," said Sangakkara. "We have to show our responsibility and do justice to the kind of seniority we have."
The Sri Lankan skipper was all praise for Muralithran, who is set to retire from international cricket after the World Cup.
"Murali is a legend to bowl virtually on one leg and still get wickets," said Sangakkara, 33.
The skipper said he was confident that Muralitharan would be fit for their quarter-final which Sri Lanka will hope to be in Colombo on March 26.
"We have a few days and will have a few tricks up our sleeve. Hopefully he will get fully fit in that time period," said the captain.
"We have fixed other guys up quickly in that kind of time. Murali needs to play. This is his last World Cup and he wins a lot of matches for us."
"He needs to have the freedom to do as he pleases. He needs to bowl and get wickets."
Muralitharan, 38, said he was confident the injury was not a serious one.
"It's not a big tear and there was just a little bit of discomfort," he said.
"I'm bowling well and the dew factor here helped me. I am used to the conditions having played a lot of day-night games in England. I wanted to bowl slower so the ball skids off the surface.
"I was able to keep a good line and length, bowl doosras and take wickets.
"After I was hurt, I got some treatment but I told the captain that I wanted to bowl. I didn't think about the pain. I just bowled."
Sri Lanka fired up by senior service
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