Victory was based firstly on some spectacular top-order batting and later by disciplined death bowling that marked the Scots out as genuine contenders for one of the two places on offer at the World Cup later this year.
However, this performance was by no means the finished article and Gordon Drummond's men were forced to dig deep before coming out on top.
They were given the perfect start by Richie Berrington and Calum MacLeod, who raced out of the traps, scoring at 10 runs an over, after Drummond had won the toss and elected to bat.
Berrington was first to depart for a 16-ball 28 and his replacement, Kyle Coetzer, was no less punishing on the Kenyan bowlers.
The Northamptonshire batsman helped himself to 46 in quick-time, stroking six boundaries and the only maximum of Scotland's innings. However, MacLeod stole the show in a man-of-the-match display which yielded 55 runs from just 35 deliveries.
The former Warwickshire all-rounder occasionally toyed with his rivals, improvising a series of wonderfully executed strokes. His effort brought seven boundaries but there will be some concern in the Scottish camp at the way momentum was lost after his departure.
Indeed, among the middle order men, only Preston Mommsen made any impression,stroking an unbeaten 22 in the closing overs.
Scotland's innings should should probably have been more substantial than the 178-7 they reached and, for a time, it looked as if it might not be enough.
Kenya's openers raced to the 50 mark in five overs without alarm, Alex Obanda and Duncan Allan – a player who sounds as if he might qualify for Scotland but whose roots are in Australia – taking a heavy toll on the Saltires bowlers. It took the introduction of Majid Haq to bring the breakthrough, the Clydesdale spinner trapping Allan in front for 18.
Obanda had moved to 35 from just 17 deliveries when he was caught by Craig Wallace off Mommsen as the Scots hit back.
However, in the experienced Collins Obuya, Kenya had a potential matchwinner and he kept his side firmly in contention with the run-rate hovering around the 10-an-over mark.
In the end, the game turned decisively in Scotland's favour when the penultimate over of the match, bowled by Drummond, went for just four runs and brought the prize scalp of Obuya.
Safy Sharif, making his official international T20 debut, never gave the Kenyans a sniff at the 21 runs they needed from his final over, the youngster finishing with 1-20 from his four overs to compliment the captain's 3-20.
Pete Steindl, the Scotland coach, said: "It was a tough start to the campaign but it's good to be up and running with a win. It's also good we were tested because there is a lot of tough cricket ahead.
"The second last over was a vital one because the game could have gone either way. Drummo just stuck to his plans and made scoring really difficult.
Scotland's 178 was the highest total by any of the 16 teams on the opening day of the competition.
However, they face another tough test today against Namibia, who produced the surprise of the day by beating the tournament favourites Ireland.