Bourke and Stevenson turned in a splendid performance to put behind them the memory of finishing second a year ago, with a withering surge over the last 500m.
They were third at that point before easing past the Polish and Australian combinations, winning in 6min 38.04s, 1.32s ahead of the Poles.
Twigg whooped in delight at her gold, having finished with bronze and silver medals at the last three worlds.
She bossed her duel with Australian defending champion Kim Crow, and had a margin of almost three seconds at the line.
Emma Twigg of New Zealand celebrates after winning the Women's Single Sculls event. Photo / AP
The win has special significance for Twigg, who is stepping aside from rowing for the next 10 months to do academic studies in Europe.
She'll then have to win her seat back ahead of the countdown to the Rio Olympics in 2016. Today's performance will, however, have been the equivalent of leaving a fat reminder card pinned to Rowing New Zealand's door.
New Zealand's other golds were won by Eric Murray and Hamish Bond, who added the coxed pair with Caleb Shepherd to their now expected coxless pair crown; Julia Edward and Sophie MacKenzie in the lightweight women's double and the women's four in the non-Olympic event.
Olympic champion Drysdale had a titanic duel with his arch rival Ondrej Synek of the Czech Republic, who prevailed by a mere .73s.
The lightweight four of James Hunter, Alastair Bond - standing in for the injured James Lassche - Peter Taylor, and Curtis Rapley were unable to peg back their Danish rivals, with whom they have had a series of tough contests in the last two seasons.
The Danes won in 5: 47.15, with New Zealand an impressive second in 5:48.76 and Britain third a further .82s back.
In the men's double scull B final Karl and Robbie Manson finished second behind Great Britain, for eighth place overall.
RNZ will name a high performance summer squad on September 10, with training to start on September 29. Regional performance centre squads for Auckland, Waikato, Central and Southern will also be named this month.