Costel Pantilimon's goal-kick reached Steven Fletcher, who headed the ball down for Defoe to beat Tim Krul with a left-footed volley.
The former Tottenham player became clearly emotional during his celebrations.
He told Sky Sports News: "To be honest it's unbelievable. As soon as it leaves your foot you know it's going in and it's an unbelievable feeling.
"Words can't even describe how I felt when that went in - it's quite emotional really.
"It was a massive game and I just wanted to do well. The lads have worked so hard and everyone's put the effort in. We just wanted the three points as well and I'm delighted we got them."