I had the same probleam yesterday, with both dll and static lib.
I didn't found a real solution but a simple workaround: recompile qwt disabling the CONFIG += QwtDll in qwtconfig.pri (it is line 78 in 5.2, don't know in 5.1)
In this manner you won't have the dll and you have to use the static lib, but at least you won't get the runtime error.