Dawson's goal broke the deadlock after Australia had opened the scoring with a field goal from Trent Mitton in the 44th minute, only for Great Britain to equalise through Mark Gleghorne in the 51st.
Nine-time winners of the Sultan Azlan Shah Cup, Australia stay atop the standings ladder with 10 points in four matches. Australia have already placed one foot in the final.
It would take a series of dramatic results, including World champions Australia's shock loss to lowly ranked Japan, for two teams to overtake them in the standings after the last round of league fixtures on Friday.
India are now No. 2 in the standings due to a one-goal advantage they have over Britain in goals scored after today's matches, although they both have the same goal difference.
New Zealand today rode on Kane Russell's 25th-minute goal to prevail 1-0 over hosts Malaysia. But they retain the fourth spot in the standings.
India's 4-3 win over Japan kept them on course for a second successive appearance in the title contest. Australia had defeated India 4-0 in the final last year.