Govers sent a stinging shot into the boards from top of the circle in the fifth minute of extra-time to clinch Australia's fifth successive Champions Trophy triumph after the teams were tied 1-1 in regulation period.
Olympic silver-medallists the Netherlands had opened the scoring in the 18th minute through a penalty corner conversion by Sander de Wijn, while Australia equalised in the 31st minute on a penalty corner strike by Russell Ford.
Australia dominated the title contest against the Dutch, who were playing their first final after six years.
Dutch custodian Jaap Stockmann, who played a brilliant game against dominant Australian strikers, was beaten by a firm shot from Govers, who had been left unmarked on top of the circle and received the ball from Eddie Ockenden.
Ockenden, captaining the Australian team in the final, shaped the winning goal through his fine move down the centre when he got past a host of Dutch defenders before finding Govers on the right flank with a measured pass that helped Australia overcome Netherlands.