The Voice Australia winner leads the tally with a cover of Lorraine Ellison's 1966 hit, which she performed during the show's semi-finals.
Eden dominates the rest of the chart, occupying a further seven spots with tracks including her winner's single 'You Won't Let Me' at number five. Her debut album My Journey will be rush-released next week.
Meanwhile, last week's chart-topper Flo Rida falls to six with 'Whistle', fellow Voice contestant Darren Percival lands at eight with 'Damage Down', and Carly Rae Jepsen's 'Call Me Maybe' dips from four to complete the top ten.
Further down the chart Keith Urban enters at 39 with 'Without You', Rudimental's 'Feel The Love' starts at 42, and fun. debut at 46 with 'Some Nights'.
The Top 10 singles in full (click where possible for our reviews):
1. (*) Karise Eden: 'Stay with Me Baby'
2. (2) Karise Eden: 'Hallelujah'
3. (*) Karise Eden: 'I Was Your Girl'
4. (*) Sarah De Bono: 'Beautiful'
5. (*) Karise Eden: 'You Won't Let Me'
6. (1) Flo Rida: 'Whistle'
7. (3) Maroon 5 ft. Wiz Khalifa: 'Payphone'
8. (*) Darren Percival: 'Damage Down'
9. (6) Chris Brown: 'Don't Wake Me Up'
10. (4) Carly Rae Jepsen: 'Call Me Maybe'
Watch Karise Eden performing 'Stay with Me Baby' below: