Sam Allardyce described his side's 4-2 win at 10-man Swansea City as "enormous" after Sunderland closed the gap on their Premier League relegation rivals to a single point.
Jermain Defoe's hat-trick at the Liberty Stadium was the difference, but a crucial turning point came in the first half when Swansea defender Kyle Naughton was harshly sent off for a tackle on Yann M'Vila.
"It's an enormous, enormous, enormous three points for us which gives us a lot of hope going forward," said Allardyce, who was taking charge of his 450th Premier League match.
"I'm delighted for the fans; they deserve that result. They can enjoy that journey home now.
"The clinical Mr Defoe won us another game. We're putting the myth to bed that Jermain can't play up front on his own.
"We've made big strides to close the gap but we have to continue to chip away."
Defoe, who scored against Swansea for the third successive Premier League match, was understandably delighted to net such an important hat-trick for his side, who cranked up the pressure on fourth-bottom Swansea.
But there was controversy over his first two goals, with the former England international appearing to be offside, although the assistant's flag stayed down.
"You have to keep making the runs - if you're offside you're offside. You get in the position and see what happens after," said Defoe.
"This is massive. The rest of the season now will be big. We have to recover and just keep doing what we are doing.
"We are delighted with the win because we needed it."
How to watch Manchester City vs Arsenal: Live streams for WSL match
‘Arsenal’s Class of ’83 would give Man United’s Class of ’92 more than a good game – It’s a scandal that youth team isn’t talked about enough, if at all’: Martin Keown believes the Gunners team he grew up with doesn't get anywhere near enough credit
