The Tigers captain timed his move to perfection to power home a cross from Ahmed Elmohamady and ultimately take his side four points clear of the relegation zone with four games to play.
And the few Liverpool fans who ignored boycott calls over the ??50 ticket price must have wished they had stayed away as they saw their own side’s slim Champions League hopes effectively end.
But Dawson’s effort capped a magnificent effort from the hosts who dominated from start to finish and successfully built on their 2-0 win at Crystal Palace on Saturday.
Steve Bruce’s men surged forward from the opening minute when an Elmohamady cross from the right was hooked clear by Dejan Lovren.
And for a large part they looked simply unrecognisable from a side whose run of six games without a win looked to have left them relegation certainties as recently as last week.
It was Liverpool, without Steven Gerrard whom boss Brendan Rodgers indicated was being rested for the increasingly inconsequential run-in, Liverpool looked rudderless and ill-equipped to cope with the hosts’ attacking intent.
Dame N’Doye, Hull’s two-goal hero on Saturday, headed a sixth-minute chance straight at Simon Mignolet from a Sone Aluko cross when he perhaps should have done better.
The visitors did briefly threaten through the energetic Glen Johnson down the left, while Philippe Coutinho came close when he scythed a shot which forced a fine reflex save from Steve Harper.
But the sporadic threat summoned by Rodgers’ men did not faze Hull in the slightest as they once again showed the character that had got them priceless points at Anfield, the Etihad and the Emirates this season.
Mignolet punched away a dangerous Robbie Brady free-kick and was grateful for a poor follow-up by James Chester, before Mario Balotelli tried a pointless back-heel 20 yards from Harper’s goal which summed up his dismal contribution to first-half proceedings.
Mignolet pulled off a superb double-save to deny first Jake Livermore then Aluko in a mighty goalmouth scramble, then had to pluck a dangerous Stephen Quinn cross from the air as the hosts continued to press.
The goal the Tigers richly deserved arrived in the 36th minute when Elmohamady lofted the ball back into the box and Dawson timed his move to perfection to spring the offside trap and belt a firm header past the visiting keeper.
Hull’s only frustration must have been that they were not ahead by more, and that danger was highlighted in first-half injury time when Johnson skipped unchallenged in from the left and rolled the ball across the goal-line where unfathomably no visiting front men were on hand to tap it into the net.
Despite a quieter start to the second period, it was still City who were showing the greater desire and Mignolet had to be alert to pluck the ball off the head of N’Doye after another fine cross from the left by Elmohamady.
Again as if to serve a timely reminder that the points were far from safe, Liverpool came close just past the hour mark when Jordan Henderson picked up Coutinho’s ball into the box and hit a low shot on the turn which was palmed out for a corner by Harper.
Aluko was almost sent clear on goal before stumbling into Martin Skrtel, while Henderson – the only man who looked remotely capable of coming to Liverpool’s rescue – had another good chance for the visitors when his low shot stung the hands of Harper.
The inevitably nervy last few minutes saw Sterling shoot straight at Harper while Tom Huddlestone could have sealed it with a long-range rocket which flashed just wide before referee Lee Probert’s whistle sparked jubilation.