Shahid Afridi was the hero for Pakistan, scoring an unbeaten 20-ball 39, hitting the winning six off the last ball of the final over to give Pakistan a 1-0 lead in the two-match series.
In all Afridi hit three sixes and two boundaries to help Pakistan overcome a tough challenge from world number one Sri Lanka who had taken the match to the final over with Pakistan needing six runs.
Sri Lanka relied on a fighting 34-ball 50 by Angelo Mathews who added 58 for the fifth wicket with Lahiru Thirimanne (23 not out) after their top batsmen failed to capitalise on good starts.
Dinesh Chandimal (22), Kumar Sangakkara (21) and Kusal Perera (15) were other notable contributors.
For Pakistan Saeed Ajmal and Sohail Tanveer took two wickets apiece.
The second and final Twenty20 will be played in Dubai on Friday.