Sunderland boss Gus Poyet hailed keeper Vito Mannone for the string of saves that helped secure a 1-0 win against 10-man Everton.
Sunderland's winner came in the 25th minute via a penalty from on-loan Swansea midfielder Ki Sung-yueng, who had gone down in the box under a challenge from Tim Howard that earned the Toffees goalkeeper a straight red card.
Despite having only 10 men from there, the hosts responded strongly and Mannone produced a series of impressive saves in the second half to help keep Everton at bay.
Asked after the match what had made the difference for Sunderland, who are bottom of the Barclays Premier League and picked up all three points for the first time in seven fixtures, Poyet said: "Concentration, belief.
"Maybe when nobody expects you to do something special, the players get together.
"And our goalkeeper was outstanding.
"Sometimes strikers get all the credit, but sometimes you need a goalkeeper to win you a game and today Vito probably won the game for us."
The build-up to the penalty being awarded saw Howard opt to play a short goal-kick to Leon Osman, who miscontrolled the ball.
That allowed Ki to claim possession and dart into the area, where he fell to the turf when Howard came out to tackle him.
Regarding that incident, Poyet said: "Everything changed with the mistake.
"I always say that sometimes I like games without accidents, but that was a big accident for us to take advantage of.
"Then, probably because of the situation we are in and probably because of how good Everton are, even with them having 10 men, we were just defending for our lives.
"This is the best team we have played against, even with 10 men."
Fifth-placed Everton went into the contest unbeaten in 10 matches and having not lost a league game at home in the whole of 2013.
Poyet added of the surprise Boxing Day triumph: "This is the best present you can ever give me, three points.
"It is a good day. It was extremely difficult against 10 men, but football is incredible and you never know what is going to happen."
Due to other results, following this win for Sunderland - their first away from home this term and just their third overall in the league for 2013/14 - the gap between them and safety has only been reduced by one to three points.
But it will have given their belief a huge boost as they continue in their quest for survival.
For Everton, meanwhile, the encounter will go down as a useful learning experience according to their manager Roberto Martinez, who felt both Howard and Osman were at fault with regard to the goal.
"We have very strong concepts for when a pass is on and what the decision will be when you receive the ball," Martinez said.
"Both players probably got their decisions wrong. But they are two players who have been reliable throughout the season, winning us so many points, and we are going to learn from this.
"The real disappointment is that we were doubly punished, with a red card and a goal. But the referee was spot on - I think he made the correct decision.
"We were then facing adversity and I couldn't be prouder of the second-half performance. I thought we deserved an equaliser.
"I think our performance in the second half was one of our strongest and we've learned a lot about ourselves.
"For me, although we don't have a point today, we have a stronger team going into the second half of the season."
Martinez confirmed Toffees forward Kevin Mirallas - who departed the pitch and headed down the tunnel for a few minutes in the first half, leaving his side with only nine men, before being substituted at the interval for Ross Barkley - had been feeling unwell.