Matt Phillips was the unmarked man in Hoops to head home from sub and debutant Nasser El Khayati's cross-cum-shot. But even then, Rs had to mount a rearguard action to hold on.
Hasselbaink reckoned the victory tasted all the more sweeter as a result.
He said: "When you go in at 0-0 you have done yourself an injustice.
"We deserved to be 2-0, or 3-0 up, but it's not about deserving, and so we kept on plugging away, and it's good it came in the last five minutes because it tells me the spirit is good, and the organisation is good.
"It was difficult in the wind, and at times you have to put the ball in the stands on a day like this.
"But it was all about belief and they can now relate to that. It's a relief for the players."
El Khayati's trickery set up the winner, but there were a few including his gaffer thinking it might have been an attempt on goal.
Hasselbaink added: "I didn't ask whether it was a cross or shot, but more importantly our wide player was at the second post."