The Canadian singer-songwriter has knocked Sigma's 'Nobody To Love' from number one, with 'Hideaway' becoming the third fastest-selling single of 2014 so far.
The track has sold 136,000 copies in the UK over the last seven days.
On scoring a number one debut, Kiesza told OfficialCharts.com: "Being Number 1 is the most amazing feeling ever. I just want to say thank you to everybody who's supported it.
"I never expected this at all when I created 'Hideaway'; it's amazing to see people come out of the woodwork and fall in love with it, so thank you!"
Sigma drop to two with 'Nobody To Love', while Shift K3y has claimed his first Top 10 hit with 'Touch' at number three.
John Legend's 'All Of Me' is a non-mover at four, while Aloe Blacc's recent chart-topper, 'The Man', drops from number three to five.
Tove Lo's 'Stay High' rises from 12 to six on this week's countdown, while Pharrell Williams is a non-mover at seven with 'Happy', and Duke Dumont drops two places to eight with the Jax Jones-assisted 'I Got U'.
Iggy Azalea and Charli XCX's 'Fancy' slips four places to nine in its second week on the chart, with Route 94 and Jess Glynne's 'My Love' completing the Top 10.
Elyar Fox's second single 'A Billion Girls' narrowly misses out on the Top 10, debuting at 11. Meridian Dan is a new entry at number 13 with 'German Whip', featuring Big H and JME.
Meanwhile, Showtek, Justin Prime and Matthew Koma's 'Cannonball (Earthquake)' debuts at number 29.
Watch the music video for Kiesza's 'Hideaway' below:
Source: Official Charts Company
View the latest Official Top 100 Singles Chart