Jordi Gomez scored a pair of penalties either side of half-time to give the Black Cats a crucial 2-1 win over Southampton at the Stadium of Light.
Despite remaining in the relegation places, Sunderland are just a point from safety and have a game in hand over Leicester and fellow Tyneside strugglers Newcastle.
And now the Sunderland players are hoping to draw inspiration from last season’s remarkable late turnaround when they won four out of their last five, including wins away to Chelsea and Manchester United.
Graham said: “We’ve got a game in hand, we’ve got Leicester at home and Everton away next week and we need to be going into those games off the back of good performances so if we can do that I’m sure we’ll be fine.
“Towards the end of last season the boys went to Man City and should have won, went to Chelsea and won, went to Manchester United and won so we’ve got to hang on to that belief that we can go to those sorts of teams and pick up points.
“Certainly the home game coming up against Leicester in between them is vital, but we just need to take one game at a time at the minute, dust ourselves off, enjoy this win and focus on next weekend against Everton which is a massive game.”
Cattermole said it was important to keep fighting and hoped players who were in the squad last season can draw on their experience of a relegation battle.
He said: “We’ve just got to keep going. We’ve done nothing yet and we just need to get through to the 24th of May and make sure we are still in this league.
“I’ve certainly learnt a lot from it (winning four out of five to stay up at the end of last season) and we’ve still got a lot of players in the dressing room who were in that position last year so we know exactly what it is all about and the importance of making sure we stay in the league.
“We’ve got four massive games left and as long as we keep focusing in training and believing, I think we look a good side.”
Graham was a real handful for the Southampton backline and he is hoping to carry that form into the remaining games of the season to help the Black Cats secure their Premier League status.
He said: “It was great to hear the fans singing my name today. I’ve had a tough couple of years at the football club.
“I’ve been in and out of squads, I’ve been out on loan here, there and everywhere but if I play like that hopefully I can stay in the team and contribute until the end of the season.”