Sunderland striker Jermain Defoe believes the players have proved they can handle the pressure of a relegation battle.
A 2-0 win at Everton meant the Black Cats recorded back-to-back victories for the first time this season and it could not have come at a more crucial time.
The result lifted Dick Advocaat's side two points clear of the relegation zone but wins for West Brom, Aston Villa and Leicester and a point for Newcastle mean the quest for survival is far from over.
"It was a must-win game to be honest, we knew we had to win," said Defoe, who made sure of three points with an 85th-minute effort after Danny Graham's fortuitous first goal for the club 28 months after joining.
"We still have an important game next week (at home to Leicester) but it is back-to-back wins and we are delighted to have done it.
"I think it has added a bit more pressure on the sides around us now.
"There was a lot of pressure on us to get a result and we handled that and that is credit to everyone at the club.
"We were solid, organised and patient as this is a difficult place to come. It was never going to be easy, so to win here 2-0 was credit to the players.
"It was impressive to get the result - it doesn't matter how you do it. There was a lot of pressure in a must-win game and we can go home happy."
Everton dominated possession but despite creating opportunities in each half, their best chances did not come until they were behind when Seamus Coleman volleyed wide and James McCarthy fired a low, angled drive against the post.
By then Graham had ended his long wait for his maiden Black Cats goal, although it was not intentional as, with his back to goal, he appeared to be trying to get out of the way of Jordi Gomez's shot when it took a deflection off his shin and looped over Tim Howard.
Everton briefly applied the pressure before Defoe, playing wide right of a three-man forward line, bundled home substitute Adam Johnson's cross with his thigh with the ball also touching his hand as it went in.
"You need a bit of luck, and yeah and I think you get that luck when you work so hard as a team," added the former England international, who joined from Major League Soccer side Toronto in January.
Advocaat is pleased with the way his three-pronged strikeforce has performed in the last couple of weeks, having beaten Southampton the previous weekend, and despite Defoe being given an unfamiliar wide role the head coach said he does not insist the striker rigidly sticks to the position.
"It is not his favourite position but we are in a position where we have to do everything for the club to stay up," said the Dutchman, who has earned 10 points from the six matches he has been in charge.
"If he scores as well it gives him a boost but he has the freedom as well to come away from that position."
After defeat at Aston Villa the previous week, Everton's season is drifting aimlessly with a top-10 finish looking almost beyond them.
"It becomes very difficult," admitted manager Roberto Martinez.
"I always felt the two home games left were very important but we are facing West Ham next week and are in a direct fight for those positions.
"I think it is important we don't lose the focus of looking for the top 10."