Put in to bat after losing the toss, Ireland soon shattered the curious strategic decision by the Ugandans with captain William Porterfield helping himself to 53 from 43 balls while Paul Stirling claimed 41 off 23.
Kevin O’Brien’s unbeaten 39 and Gary Wilson on 30 helped the Irish finish their 20 overs with a score of 179 for five.
Uganda were bowled out just over the halfway line in their quest for 180, with O’Brien again doing plenty of damage by claiming two wickets in seven deliveries.
George Dockrell was three for 26 as the African nation finished on 97.
Ireland remain with a chance of finishing top of the group, should they defeat Oman and unbeaten Namibia lose to Italy in the final round of games before the play-offs.
Ireland lost their opening game by four runs to Namibia.
Opener Richie Berrington hit a match-winning 67 to help chase down Italy's 136 for eight with two overs to spare.
Off-spinner Majid Haq was the pick of the bowlers as he claimed two for 16 from his four overs, while Matthew Parker snared two for 24 from three.
The win moves Scotland above the Italians and into third place in Group B - the final qualification position for this week's play-offs.
Victory over the lowly United States in their final group game on Tuesday will ensure Scotland reach the play-offs.
Six teams will compete in the play-offs for the two qualification places at the World Twenty20 in Sri Lanka, which starts on September 18.
Hong Kong 103-9, 20 overs (Irfan Ahmed 54; Dollat Zadran 5-14, Izatullah Dawlatzai 2-19)
Afghanistan 104-1, 11.1 overs (Karim Sadiq 22, Javed Ahmadi 38 n.o., Mohammad Shahzad 43 n.o.)
Man of the Match: Dollat Zadran (Afghanistan)
Nepal 85-7, 20 overs (Gyanendra Malla 32, Basanta Regmi 20; Michael Swart 2-13)
Netherlands 86-4, 13.5 overs (Basanta Regmi 3-32)
Man of the match: Michael Swart (Netherlands)
PNG 155-6, 20 overs (Vani Vagi Morea 49 not out, Chris Amini 32, Geraint Jones 23; Curt Stovell 2-21, Sam Robinson 2-27)
Bermuda 158-5, 19.3 overs (Janeiro Tucker 52 not out, Curt Stovell 31, David Hemp 30)
Man of the match: Janeiro Tucker (Bermuda)
Canada 178-3, 20 overs(Ruvindu Gunasekera 95, Hiral Patel 43)
Denmark 123-4, 20 overs (Rizwan Mahmood 65, Freddie Klokker 40; Henry Osinde 2-16)
Man of the Match: Ruvindu Gunasekera (Canada)
Italy 136-6, 20 overs (Gareth Berg 29, Peter Petricola 28, Carl Sandri 25; Majid Haq 2-16, Matthew Parker 2-24)
Scotland 137-3, 18 overs (Richard Berrington 67, Preston Mommsen 36)
Man of the match: Richard Berrington (Scotland)
USA 90 all out, 18.2 overs (Sushil Nadkarni 41; Ragheb Aga 3-16, Nelson Odhiambo 3-13)
Kenya 93-1, 10 overs (Duncan Allan 34 not out, Collins Obuya 24 not out, Alex Obanda 34)
Man of the match Nelson Odhiambo (Kenya)
Namibia 120-7, 20 overs (Sarel Burger 53, Gerrie Snyman 29; Farhan Khan 2-14, Ajay Lalcheta 2-13)
Oman 84, 18.4 overs (Christi Viljoen 4-8, Sarel Burger 3-14)
Man of the Match: Sarel Burger (Namibia)
Ireland 179-5, 20 overs (William Porterfield 53, Paul Stirling 43, Kevin O’Brien 39 not out, Gary Wilson 30; Jonathan Sebanja 2-9)
Uganda 97 in 19.5 overs (Jonathan Sebanja 20; George Dockrell 3-26, Kevin O’Brien 2-7, Trent Johnston 2-8)
Man of the match: Kevin O’Brien (Ireland)