Jayawardene was unbeaten on 149 as Sri Lanka, taking advantage of a butter-fingered English display, carried their overnight score of 147-4 to an almost impregnable 384-6 by stumps on the rain-hit second day.
Play began 90 minutes late due to a wet outfield caused by heavy rain on Tuesday evening, further curtailing a match in which just 55 of the stipulated 90 overs were bowled on the first day.
Jayawardene, who became Sri Lanka's leading run-getter during his 195 in the drawn second Test, surpassed Aravinda de Silva's record of 20 centuries with his second consecutive ton.
His five-hour knock, studded with 15 boundaries, gives the hosts a chance to press for a 2-0 series win over the remaining three days and clinch second place in the official rankings behind Australia.
"We are positive about trying to win this one because we go to every match wanting to win it," said Jayawardene.
"The wicket is good for batting but it will deteriorate as the match progresses and probably