This happened to me many years ago on a Canadien flight from Ottawa to Toronto.
Only it was a massive aircraft, probably 250+ seats, with more than half a dozen flight crew, 100% empty except for us. It was going on to Vancouver we were told.
It was the last flight of the night and we were told the earlier flight was delayed so they moved all the other passengers onto that one as it left just before ours. We were a little late getting to the gate, so we had our own plane all to ourselves.
The icing on the cake was both my wife and I also got to ride in the cockpit - her for the take-off, and both of us for the landing. Way cool.
Them was the days, eh?
Cheers,