Sunderland boss Sam Allardyce remains optimistic the goals of Jermain Defoe will keep his side in the Premier League.

Defoe was on target at Carrow Road on Saturday, netting the second as Sunderland beat relegation rivals Norwich City 3-0.

The former Tottenham striker grabbed his 13th goal of the season and Allardyce believes his prowess, allied with more clean sheets, is a recipe for success as the Black Cats attempt to drag themselves out of the mire.

He said: "The clean sheet was the first thing I have been asking for between now and the end of the season as they will keep us up.

"We have a goalscorer that's into double figures in a team that's been in the bottom three all season.

"If we can keep clean sheets, Jermain Defoe scores one goal and that wins us games, that's the belief he gives us.

"The myth has been put to bed that he can't play up front on his own. Since we did it – and it took me a while as everyone said he couldn't do it – he's continually scored goals.

"We have to play a different way as you can't play off him, you have to play wide and through midfield, but he will score the goals."

The win, which also featured goals from Fabio Borini and Duncan Watmore, moved Sunderland within a point of Norwich and safety. The Wearsiders also have a superior goal difference, thanks largely to their efforts on Saturday, and a game in hand.

Allardyce added: "Goal difference could be a factor. If you offered me the option of staying up on goal difference I'd take that right now if I could.

"But now it's only one point, with a good goal difference and a game in hand. If we can pick up some points against Arsenal next weekend we'll be rushing back in to see what the results have been elsewhere.

"We should take a lot of confidence from the win. For this weekend we can relax and enjoy ourselves."

Allardyce also played down an early incident which saw both benches square up after Robbie Brady's senseless challenge on DeAndre Yedlin which sent the young American full-back flying headlong into an advertising hoarding.

"I was a bit disappointed the fourth official didn't stop the Norwich players encroaching into my box," he said.

"I was protecting my box and my player. I got a bit carried away with all the emotion in the game."