Hull midfielder Ahmed Elmohamady would like to see Wednesday night's opponents and Premier League relegation rivals Middlesbrough appoint Steve Agnew as permanent boss. It is a big, big game for us and we need three points.
Hull now sit on 30 points having played 31 matches and captain Dawson is confident they can go on to retain their top-flight status.
The Tigers' fifth win in six home league games lifted them two points above Swansea, while Middlesbrough, without a league win since December 17, are seven points from safety and appear destined for a return to the Championship.
Marco Silva's side trailed to Alvaro Negredo's opener, but Lazar Markovic equalised before Oumar Niasse and Abel Hernandez put Hull in control at the KCOM Stadium.
Boro were stunned and needed some invention to get back in the game and Rudy Gestede almost provided that but he saw his header tipped onto the crossbar by keeper Eldin Jakupovic.
Silva, on the other hand, was able to reflect on a second-successive victory for his team, but reaffirmed that Hull must continue to improve if they are to move clear of the bottom three. Grosicki popped up on the right wing to collect a fine pass from Harry Maguire and deliver a handsome ball across the face of goal to Hernandez who did the rest at the far post.
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Adama Traore's low angled cross from the right side of the penalty area was turned home at the far by the unmarked Negredo.
"We scored just before half-time and maybe the whistle came at a bad time for us - we were on top and had them penned in".
The end-to-end stuff continued unabated as a Middlesbrough surged forward, Rudy Gestede's goalbound header being tipped onto the bar by Hull 'keeper Eldin Jakupovic.
Middlesbrough reduced the deficit in first-half stoppage time in controversial circumstances.
A touchline conflab between Michael Oliver and his linesman gave Hull hope that justice would be done, but the goal stood despite replays clearly showing the Dutch defender had been two yards offside when Gibson headed the ball in his direction.
A free kick from left was beautifully delivered to the far post by Robertson and Maguire produced a wonderful header back across Valdes and into the far corner of the net.