Ireland downed Hong Kong by 85 runs for its seventh successive victory while Afghanistan defeated Kenya by 34 runs that gave the Asia side its sixth win in seven matches.
Sunday's results mean Ireland and Afghanistan have topped their respective groups and, as such, have qualified automatically for the event proper.
This is Ireland's fourth successive qualification for the World Twenty20 having played in the 2009, 2010 and 2012 tournaments, whereas for Afghanistan, it will be the third time when it will feature in the event after appearing in the West Indies and Sri Lanka editions.
With four places still up for grabs, Hong Kong will now face Nepal and the United Arab Emirates (UAE) will square off against the Netherlands on Wednesday with the two winners also qualifying for the Bangladesh event that will be staged from 16 March to 6 April.
At Zayed Cricket Stadium, Paul Stirling was in devastating form when he smashed a 46-ball 77 with five fours and a six as Ireland scored 207 for 4 and then returned figures of 4-0-10-4 to help Ireland collect its 17th consecutive victory in the ICC World Twenty20 Qualifier.
Electing to bat first, Stirling and William Porterfield (38) put on 91 runs for the first wicket, while for the fourth wicket Kevin O'Brien (62 off 27 balls with three fours and five sixes) and Gary Wilson (19) added 39 runs for the fourth wicket in almost two overs.
Ireland scored 70 runs off the last five overs, including 24 off the final over in which O'Brien clobbered three sixes and a four off Munir Dar who finished with figures of one for 49.
Hong Kong made a brisk start and reached 92 for two in the 10th over before Stirling got his acts together and broke the batting side's back by claiming the wickets of Jamie Atkinson (48), Nizakat Khan (13), Mark Chapman (one) and Tanwir Afzal (two) as Hong Kong was bowled out for 122 in 17.1 overs with the last eight wickets falling for 30 runs in just over seven overs.
Stirling was well supported by left-arm spinner George Dockrell who picked up the scalps of Munir Dar (seven) and Aizaz Khan (six).
Kenya, in its chase, was spun out by Samiullah Shenwari who recorded his Twenty International (T20I) best figures of five for 13 as the African side was bowled out for 114 with 10 balls to spare.
Rakep Patel was the only batsman to offer any resistance when he scored 52 off 38 balls with two fours and three sixes, while Steve Tikolo was the other batsman to reach the 20-mark when he slapped five fours in a 20-ball 25.
In the other matches of the day, Canada defeated Italy by five wickets at Zayed Cricket Stadium, Abu Dhabi; Namibia defeated Uganda by 38 runs at Abu Dhabi Oval 1; United Arab Emirates (UAE) defeated United States of America (USA) by 14 runs at Abu Dhabi Oval 1; Scotland defeated Denmark by 75 runs at ICC Academy Oval 2, Dubai; and PNG defeated Bermuda by 25 runs at ICC Academy Oval 2.
Ireland, Afghanistan qualify for 2014 ICC World Twenty20
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