The former Sri Lanka captain, who opened the innings after Sanath Jayasuriya fell sick, scored a sublime 123 as the hosts overhauled Pakistan's 288 for eight with 21 balls to spare.
Jayawardene compiled a 202-run partnership for the first wicket with Upul Tharanga, who scored 76.
Victory gave Sri Lanka an unassailable 3-0 lead in the five-match series, their first ODI series win against Pakistan on home soil.
Jayawardene's century, an innings that was hampered at the end by painful leg cramps, was the 11th of his career and his first since 2007.
Pakistan hopes were briefly buoyed after the fall of three quick wickets, Sri Lanka sliding from 202 without loss to 212 for three.
However, skipper Kumar Sangakkara finished off the game with an unbeaten 37, adding 56 with Thilina Kandamby (32) for the fourth-wicket.
Umar Akmal top-scored with a brisk 66 for Pakistan and his elder brother Kamran Akmal chipped in with 45, sharing a 71-run second-wicket partnership with skipper Younus Khan, who scored 44.
Pakistan's lower order also rallied, with Shahid Afridi (32), Abdul Razzaq (30) and Naved-ul-Hasan (30 not out) all making contributions.