Middlebrough boss Gareth Southgate hailed his players' efforts in the win over Hull but warned those standards need to be maintained if they are to stay up this season.
The Boro boss signalled his intent from the off in the home tie at the Riverside Stadium as he fielded Afonso Alves, Jeremie Aliadiere, Marlon King and Tuncay Sanli in attacking positions against City.
And the home side's highly energetic start was soon rewarded with an opener from Turkish forward Tuncay as he latched onto an Alves effort which was parried first by City's Matt Duke.
Just as Boro started to become more confident, the Tigers equalised in the ninth minute when on-loan striker Manucho connected with a Nick Barmby cross to head home the equaliser.
But Matthew Bates soon got the Teessiders back in front with a clinical effort and once former City striker King had slotted home in the second half, there was no way back for Hull.
On the win Southgate told Sky Sports: "It's crucial for us there's no doubt about that.
"To keep any hope alive we had to win today. The players have given a fantastic performance, totally committed.
"Our energy levels were fantastic, we had good pace throughout the team today, we took our goals well and we stood up to the challenge. We had to be men today.
"We needed a performance that showed our fans how much it meant to us to play for the shirt and right through the squad they did that.
"It's great credit to my staff because all week they've been brilliant, they've put an unbelievable amount of hours in and we got the response that we needed today and we've given ourselves hope. You just never know in football."
The win puts Middlebrough just two points behind 17th placed Sunderland after their rivals lost to Premier League champions Manchester United.
But Southgate has warned his players and fans not to get carried away with the vital win and stick to the job in hand.
"Nobody here is going to get carried away with anything, we still have it all to do," he said.
"The last few weeks in particular, with the rest of the country writing us off, I think our fans have rallied behind the cause.
"We didn't reward that in the last two matches away from home but we rewarded it today and we've got to do it again with everybody pulling in the same direction.
"It'll be interesting in one or two other dressing rooms now.
"If the season finished tomorrow we'd be out of the division so to a degree we've got nothing to lose."