Ending a run of four straight defeats, Steve Bruce's men drew 1-1 with Everton at Goodison Park after a strike around the hour mark from substitute Sone Aluko cancelled out Romelu Lukaku's first-half opener for the hosts.
Hull - above the relegation zone on goal difference alone - have also secured creditable draws at Arsenal and Liverpool this term.
But Dawson sees the truly vital fixtures for the team being those where they are taking on outfits lower down the table.
Hull boss Steve Bruce stressed after Wednesday's match that the points his side claimed from such matches last term, their top-flight comeback season, were ultimately the reason they beat the drop.
And when asked if games like Saturday's visit to the KC Stadium of West Brom are what will define Hull's 2014-15 campaign, Tigers centre-back Dawson said: "Yes, of course they are.
"You look at our recent performances away from home, when we have been to the Emirates Stadium, Anfield and now Goodison Park, and we have taken a point each time.
"We can take a lot out of this - even in the first half (against Everton), with as much possession as they had, how many shots did they have on goal? Not too many.
"But yes, the games against the likes of West Brom and other teams that are going to be around us are where we really need to pick up the points."
While it proved a constructive evening for Hull, Wednesday was frustrating for Everton, who had looked well in control in the first half but faded badly as the contest wore on and were booed off at the end by some fans.
Toffees boss Roberto Martinez - whose side have been playing in the Europa League group stages on top of their domestic fixtures, qualifying for the knockout rounds - admitted tiredness had been a factor.
The Merseysiders have also had injuries to contend with, but Everton defender Sylvain Distin says the squad must keep pushing on, with a tough-looking trip to Manchester City on Saturday up next.
Reflecting on the Hull game, Distin told evertontv: "It was very frustrating.
"We didn't lose the game but we feel like we have lost
We felt the frustration from the fans as well.
"Hull made it tough for us and it was difficult to play forward at times.
"We have had a lot of games and that's going to continue.
"We have to move on because it is a big game this weekend, then next week, then the following weekend."
Meanwhile, Hull midfielder Mohamed Diame is set for scans on his knee after limping off in the Everton game due to an ongoing tendon problem.
And Bruce fears Diame could be out for as long as six weeks.
The manager said: "It's been an ongoing tendonitis problem and the alternative may be an injection.
"That could rule him out for a month or six weeks.
"We'll have some more scans and see how he is."
Bruce also said a knee injury that forced David Meyler off only appeared to be a nasty cut.
Source : PA
Source: PA