Graham has struggled to score goals for the Black Cats ever since his move from Swansea City in January 2013.
On Saturday, the Englishman scored his first Premier League goal since December 2013, as Sunderland got the better of Everton 2-0 away from home at Goodison Park.
Defoe, who was also on target against the Merseyside outfit, was pleased to see Graham finally score for the Black Cats and highlighted his hard work during the game.
“It doesn't matter how they go in,” the 32-year-old told Sunderland’s official website after the match on Saturday.
“People might say 'it was a deflection' [for the first goal], but as a forward you've got to recognise the ball can come into an area and be in the right position to score.
“Danny did that and he's put so much work in. We needed that little bit of luck and we got that today.”
The win means that Sunderland are 16th in the Premier League table at the moment with 36 points from 35 matches.
The Black Cats are just two points above the relegation zone, but they do have a game in a hand.
There is no doubt that Graham has been a ‘flop’ at Sunderland, but his goal against Everton will have increased his confidence.
It will now be interesting to see if manager Dick Advocaat maintains his faith in the former Middlesbrough and Watford striker for their final three games of the season.