On the back of two straight league defeats, the defender was delighted with the 2-0 triumph.
"We battled hard and got the victory in the end, which was important for us," Woodgate told Spurs TV Online. "You can't always play well and it was important that we got the three points despite not playing well.
"They're going to be a threat and Steve Bruce has got them playing well. In the game we rode our luck and Gomes kept us in the game.
"The most important thing was that we got the three points going into the international break and we're back in the top four now."