Forwards Nikica Jelevic and new signing Dame N'Doye both got on the score sheet in Hull's 2-0 win over Aston Villa on Tuesday, which lifted Steve Bruce's side to 16th in the table.
N'Doye had only met his team-mates for the first time on Saturday following his move from Lokomotiv Moscow, but assisted Jelavic's opener before netting his own.
Dawson has noticed various improvements to their game after they previously drew 1-1 at Manchester City, when only a late James Milner free-kick denied them maximum points.
"The win on Tuesday was massive for us, especially on the back of last Saturday," Dawson told the club's official website.
"Obviously we got the point at Manchester City, although we know we could have had all three points there.
"But Tuesday night against Villa was vitally important for us and the two boys up front set the tone for us in that one.
"We've shown the grit and determination, yes we'd like to be a little bit better on the ball, but we saw on Tuesday that when we get the ball to the two up top, they can be a real handful.
"We've got some more big games coming up and all we can do is concentrate on ourselves, but we know that if we keep performing like we have done in the last two then we'll be alright and we’ll climb up the table."
