A possible workaround to prevent opening a new tab is to use "Save Link As" in the right-click context menu instead of left-clicking the link.

Click Start, select “Control panel” option

   Open “Uninstall a program”
   Uninstall all suspicious and unknown applications
   Reset Firefox settings
   Download AdwCleaner and scan your computer
   and remove any malware found

You must Intercept the download links.

   You must send the link to a new tab when 

it is clicked, and not just modify it with target="_blank". The tab must be opened with javascript, so that javascript will be allowed to close it when the time comes.

   Your script must also run-on / handle the 

"popup" tab, so that it can detect when to close the popup.

For this discussion, refer to

this test page at jsFiddle. 

It is structured like this:

where the a.dwnPageLink

links each open a "Download page"
-- which automatically starts a 

file download after a short delay.

Dinushi Dhananjani said

You must Intercept the download links. You must send the link to a new tab when it is clicked, and not just modify it with target="_blank". The tab must be opened with javascript, so that javascript will be allowed to close it when the time comes. Your script must also run-on / handle the "popup" tab, so that it can detect when to close the popup. For this discussion, refer to this test page at jsFiddle. It is structured like this:

• <a class="dwnPageLink" href="http://fiddle.jshell.net/cDTKj/show/"> Test file, download page at jsFiddle </a>
• <a class="dwnPageLink" href="http://dw.com.com/redir..."> TextPad (a great text editor), download page at CNET / Download </a>

where the a.dwnPageLink

links each open a "Download page"
-- which automatically starts a 

file download after a short delay.

cor-el said

A possible workaround to prevent opening a new tab is to use "Save Link As" in the right-click context menu instead of left-clicking the link.

Dosn't seem to work when trying to download video files.

Reset the browser.

   1.Go to about:config via your Address Bar.
   2.Press the button saying you'll be careful.
   3.Search for browser.newtab.url.
   4.Right click -> Reset.
   5.You might also want to check for any prefs Trovi has set. ...
   6.You might have to restart Firefox for this to work.

browser.newtab.url was not found in search

If you left-click a link then Firefox will first try to open the link in a new file. If Firefox notices that it can't display the file then you get a download dialog, but Firefox may not close the tab. If you can't right-click and use "Save Link As" as a workaround then you will have to close the tab manually yourself.

I don't know if there are extensions that will close the tab automatically in this case.