Captain Malinga grabbed 4-26 while Kulasekara picked up 3-10 as the islanders successfully defended a below par score of 129-8, restricting the UAE to 115-9 at the Sher-e-Bangla National Stadium.
Skipper Amjad Javed claimed 3-25 to lead a spirited UAE attack as the fancied Sri Lankans collapsed from a respectable 68-0 to a modest total that raised the prospect of an upset.
But Malinga and Kulasekara put the result beyond any doubt with fiery opening spells.
Malinga struck twice in the very first over playing his first match since he injured his knee during Sri Lanka’s home series against the West Indies last year.
Kulasekara, who also made a comeback after missing the recent series in India, complemented his skipper with a double strike in his second over to leave the UAE wobbling at 16-4.
Indian origin Swapnil Patil provided some resistance with 37 off 36 balls before Malinga returned in his second spell to see off the threat.
“I have still not fully recovered,” Malinga said after the match.
“I wanted to play this match and help other players and show them you can do whatever the team needs,” he said.
Earlier, Sri Lanka made a promising start as Dinesh Chandimal and Tillakaratne Dilshan put on a fifty partnership in the opening stand before they found going tough against some disciplined Emirates bowling.
Medium pacer Amjad forced a catch from Dilshan (27) at midwicket to break the partnership and then added Milinda Siriwardana and Chandimal to his tally to trigger the collapse.
Chandimal made 50 runs for Sri Lanka facing 39 balls but fell to the next ball after he reached the milestone.
His second Twenty20 fifty in 35 matches included seven fours and a six.
UAE skipper Amjad took positives from their bowling performance despite the loss.
“The whole game was excellent,” he said. “We put them [Sri Lanka] under pressure with the bowling.
“It was a big setback to lose two wickets to Malinga in the first over. Then we lost two more wickets and it is always difficult to chase.”
Mohammad Naveed and Mohammad Shahzad followed the good work of their captain to take two wickets each and stemmed the Sri Lankan run-flow.
The UAE will face hosts Bangladesh in their next match on Friday.