After a goalless first half, Mel Clewlow, who scored England's only goal in September, sent a long clearance out of defence which found Cullen unmarked on the half-way line. She tore through the Australian defence and slipped the ball in.
Slough's Jane Smith extended the lead 10 minutes later at one of only three England penalty corners with a cool conversion.
Australia responded within two minutes when a momentary lapse of concentration in the England defence allowed Katrina Powell a shot from the edge of the circle to beat Carolyn Reid. The Australians now tore into England, mounting considerable pressure in the closing minutes as they strove for the equaliser.
However, England's defence held firm with Clewlow, Lorraine Catchpole and Reid the pick of a solid team performance as they coped confidently with the assault, holding out for a rare but deserved victory.
The result was a big disappointment to the Australian coach, Ric Charlesworth, who was celebrating his 200th game in charge, and this was only his 22nd defeat.
Charlesworth, an ex-Australian captain, doctor of medicine and former Australian MP, has announced that he will end his successful eight-year reign as coach after next year's Sydney Olympics. As coach he has won two world titles, plus Olympic gold in Atlanta in 1996.
The teams move on to Brisbane for the second Test tomorrow.
ENGLAND: H Rose (Duke University, US); L Catchpole (Ipswich), S Chandler (Slough), F Greenham (Slough), K Walsh (Hightown); L King (Ipswich), J Smith (Slough), L Newcombe (Clifton Scottish Life ); J Sixsmith (Sutton Coldfield), T Cullen (Hightown), A Bennett (Slough). Substitutes used: K Brown (Slough, capt), M Clewlow (Canterbury), P Miller (Fyffes Leicester), M Nicholson (Slough), C Reid (Hightown).