Beginning on the back nine, Alker scored bogeys on the 12th, 15th and 18th, along with a birdie on the 17th to put him at two-over after nine holes in what was a bumpy start to the third round.
The round became a lot more bumpy for Alker as he arrived at the par-four first hole.
His drive went into the bushes, requiring two shots to get it back onto the fairway before finishing with a triple-bogey.
Things went from bad to worse for Alker at the par-three third hole.
Thrice his ball landed in the water from the tee box, before some putting woes compounded his issues, finally sinking the ball on his ninth shot of the hole to register a sextuple bogey.
He had another bogey on the fourth hole, before stringing a sequence of pars together and finishing the disastrous round with a bogey on the ninth hole.
American Kevin Chappell leads the tournament at eight-under, one shot ahead of South African Branden Grace and American John Huh.
Fellow New Zealanders Tim Wilkinson and Danny Lee both missed the cut.