Seamer Abdur Razzaq claimed three wickets as Pakistan bowled and fielded aggressively to restrict Sri Lanka to 138-6, then coasted home easily with eight deliveries to spare.
Shahid Afridi hit an unbeaten 54 off 40 balls, his second consecutive half-century, and former captain Shoaib Malik made 24 not out during a match-winning partnership of 76 for the undefeated third wicket.
Pakistan, runners-up to India in the final of the inaugural World Twenty20 in South Africa two years ago, ended Sri Lanka's unbeaten run in the tournament with style.
Pakistan last won an offical multi-nation tournament in 1992 when Imran Khan's team lifted the World Cup by beating England in the final at the Melbourne cricket ground in Australia.
The win by Younus Khan's team gave Pakistanis back home reason to cheer as the cricket-mad nation has been deprived of international tours due to security concerns in the volatile nation.
The International Cricket Council has already ruled out holding World