Each side play the other twice in the preliminary league, with the top two qualifying for the final on August 28.
Sri Lankan opener Tillakaratne Dilshan did the bulk of scoring in the initial overs, racing to 44 off 52 balls before being bowled by seamer Scott Styris.
Dilshan hit eight fours, including four in a row off paceman Kyle Mills.
Styris got his second wicket when he removed Kumar Sangakkara, the skipper, who fell to a diving catch by Nathan McCullum in the covers after hitting four boundaries in his 59-ball 40.
Jayawardene continued to gather runs comfortably and completed his half-century when he lofted off-spinner McCullum for a four.
He also hit a six off the same bowler, swinging over mid-wicket.
New Zealand made three changes from the team that lost to the hosts by three wickets in their previous match, replacing Martin Guptill, Tim Southee and Andy McKay with Peter Ingram, Jacob Oram and Grant Elliott.
Sri Lanka, who lost to India by six wickets on Monday, brought in Ajantha Mendis, Rangana Herath and Silva in place of Dilhara Fernando, Suraj Randiv and Thilan Samaraweera.
Off-spinner Randiv was banned for one match for apparently bowling a deliberate no-ball in the last game against India to leave Virender Sehwag stranded on 99.