It's possible to do this with a script for AutoHotkey (Windows automation software). Just open notepad, paste the code below and save it with the .ahk file extension. I could only test it on Windows 7 though. But it opens the search URL on a new tab as expected. The search dialog box looks like this:

global MySearch
Gui, Margin, 9, 10
Gui, Font, s12
Gui, Add, Edit, vMySearch w400 -WantReturn
Gui, Font, c999999 s7
Gui, Add, Text, Y+3, Press <ctrl> twice to hide/show.
GuiEscape:
Gui, Hide
#ifWinActive Google Search
NumpadEnter::
Enter::
submitSearch()
return
#IfWinActive
Ctrl::
KeyWait, Ctrl
KeyWait, Ctrl, D, T0.12
if ErrorLevel = 0
{
if WinActive("Google Search")
Gui, Hide
else
Gui, Show,, Google Search
}
return
submitSearch(){
Gui, Submit
searchURL := "https://www.google.com/#q=" . urlEncode(MySearch)
Run, %searchURL%
GuiControl,, MySearch
}
urlEncode(url){
VarSetCapacity(Var,StrPut(url,"UTF-8"),0),StrPut(url,&Var,"UTF-8")
While Code:=NumGet(Var,A_Index-1,"UChar")
Res.=(Chr:=Chr(Code))~="[0-9A-Za-z]"?Chr:Format("%{:02X}",Code)
return,Res
}