The UAE raised the prospect of a shock win by restricting Sri Lanka to 129-8, but the Malinga-led attack held the Emirates to 115-9.
Nuwan Kulasekara gave handy support to new-ball partner Malinga with 3-10.
Malinga undermined the UAE's chase in the first over, when he trapped opener Rohan Mustafa, and bowled the latter's replacement, Mohammad Shahzad.
The UAE recovered thanks to Swapnil Patil, who hit his team's top score of 37 off 36 balls, and lifted his team to 85-6, needing 45 more runs in 21 balls. But Malinga got Patil caught and bowled, and ended UAE hopes.
Earlier, Sri Lanka openers Dinesh Chandimal, who smashed 50, and Tilkaratne Dilshan, who added 27, combined for 68 inside 10 overs. But after they were out, the UAE put the brakes on Sri Lanka and set a target it could chase.
Chandimal sent the ball across the rope seven times and smacked one six. He looked in utter control until medium-pacer Amjad Javed appeared.
Javed inspired the UAE, using short balls to good effect by picking up three wickets in three consecutive overs to reduce Sri Lanka from 67-0 to 89-3.
Pacers Mohammad Naveed and Mohammad Shahzad then strangled the strong Sri Lankan batting line up by grabbing two wickets each.
Sri Lanka batted out the 20 overs, and looked vulnerable, but Malinga bowled the first over in reply with success, Nuwan Kulasekara was almost unplayable, and spinner Rangana Herath tormented the inexperienced UAE batsmen by his turn and guile.
Images & inputs: AP