Stevenson and Eve Macfarlane took out the women's double, beating Lithuania by 1.13s with a further 0.63s back to Britain, and easily booked a spot at next year's Rio Olympics.
The men's lightweight four of Rapley, James Lassche, Alistair Bond and James Hunter also qualified for the finals and for next year's Olympics.
Former Tauranga resident Mahe Drysdale won and remains on course to complete a record sixth world single sculls title. He is level with German Peter-Michael Kolbe who won five between 1975 and 1986.
Elsewhere, New Zealand will contest 10 out of 14 Olympic-class finals over the next two days and could equal their London effort by qualifying 11 boats for the Rio Games, if the men's quadruple sculls get second or better in their 'B' final and the eights finish in the top five.
They will have the option of qualifying three more - the women's single sculls, men's lightweight double sculls and men's coxless four - at regattas of death in Brandenburg and Lucerne next May.
Thrilling racing pervaded the semi-finals with each of four New Zealand crews finishing third or better to make their respective finals.
Details at: rowingnz.kiwi