You can use
dconf-editor to rearrange the search results in Unity dash home.
Install dconf-editor by clicking on this big button:
Or by running this command in a terminal:
sudo apt-get install dconf-tools
Then navigate to
Dash and change the setting for
['files.lens', 'applications.lens', 'music.lens'].
If you would like to get back to the default setting, you can hit the Set to Default button on the lower right corner.
This is what you get once you adjust the setting as above:
Alternatively, if you don't like to hunt with your mouse, you can run this command in a terminal:
gsettings set com.canonical.Unity.Dash home-lens-ordering "['files.lens', 'applications.lens', 'music.lens']"
It will order the results in the way you prefer.
To reset the setting, you run this command:
gsettings reset com.canonical.Unity.Dash home-lens-ordering