Hull head coach Marco Silva maintained the job was far from finished after his side climbed out of the Premier League's bottom three for the first time since October with a 4-2 home win against Middlesbrough.
Lazar Markovic cancelled out Alvaro Negredo's early opener for Boro and further goals from Oumar Niasse and Abel Hernandez gave Hull a two-goal cushion in a rip-roaring first 45 minutes.
Marten De Roon's controversial header in first-half stoppage-time gave the visitors hope, but Hull restored their two-goal lead midway through the second period through Harry Maguire's thumping header.
When asked how it felt to be out of the relegation zone, Silva said: "It's important, but nothing is finished.
"We need to continue to do our work. It will be a big fight until the end of the season, I don't have doubts about that.
"Of course it's good for our players and fans as well when we look at the table and see our position, but only that."
The Tigers have now taken 16 points from a possible 18 in their last six home league games to give their survival battle real momentum and Silva said his side's display was their best since he took charge in January.
"Since we arrived I think this is our best game," he said. "We started fast, good intensity, good rhythm.
"Some players were at a very good level, a very good performance and as a team we were strong, with a good attitude and spirit and of course I'm very happy and the players are."
In contrast to the Tigers' impressive home form, they have only won one league game on the road this season and Silva stressed the importance of picking up points on their travels.
"We need to continue our progress, step-by-step, day-by-day, to prepare for the other games," added Silva, who felt De Roon was clearly offside when he headed home Boro's second goal just before the break.
"To give ourselves a very good chance, we need to change our form away as well."
Defeat for Boro, without a league win since December 17, has left them seven points adrift of safety with eight games left to play.
But caretaker boss Steve Agnew refused to concede defeat in his side's bid to escape the drop.
"It's difficult and it's a huge challenge, but it's not one that we can't achieve," Agnew said.
"It's a group of players that will fight to the very end and we have a game in hand on some teams and a home game (against Burnley) coming up on Saturday."
Boro, who have taken one point from three games since sacking Aitor Karanka last month, were backed by 2,500 travelling fans at the KCOM, where Agnew spent over two years as assistant boss to Steve Bruce.
"After the game it was silent, you would expect that," Agnew added.
"The players are bitterly disappointed, as we all are, but we have to stay with it and dust ourselves down.
"The fans were fantastic. The players remarked on the noise they made in the far corner.
"The players wanted the performance not just for themselves, but the supporters and we have to give them something back on Saturday."