A win would give the hosts a 2-0 series success and lift Jayawardene's men past India, South Africa and England in the International Cricket Council's (ICC) Test rankings.
England would take the reverse route, going down to five from the current number two, if they lost the Test.
A win or a draw, however, would help Michael Vaughan's team retain their second spot, according to an ICC release.
England coach Peter Moores said his team had no option but to fight for a series-levelling win at the Galle International Stadium.
"We desperately want to stay up those rankings," said Moores.
"But the immediate thing is to win Test matches in the series you are playing in.
That affects your ranking. It is an indicator of where you are at at any given time.
" Jayawardene said his team deserved to go up the rankings if they won the match and took the series 2-0.
"We have played consistently well over some time now," he said.
"The important thing is to continue the same form