Sports picture of the day: GB women are Olympic hockey champions
Nicola White's last-quarter strike levelled the match at 3-3 and the game went to penalties.
Helen Richardson-Walsh converted a penalty flick after Georgie Twigg was fouled and Webb kept her cool to net the decisive effort after Hinch had time and again denied the Dutch.
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Hide AdIt meant Britain, London 2012 bronze medallists, were champions as Holland's bid for a third successive Olympic gold came to an end.
Lily Owsley, Crista Cullen and White scored in normal time, when Hinch continually kept Britain in the contest, while Kitty van Male scored twice and Maartje Paumen once for world champions Holland.
Britain's task of bringing home the gold was always going to be a tough one as none of the players in the Dutch squad at the time had ever lost a match at the Olympics.