Wilkinson, who has previously played on the PGA Tour, had rounds of 67, 70, 71 and 69 for a seven under par total to finish safely inside the qualifying mark.
After finishing 59th on the second-tier web.com Tour, Wilkinson earned his shot at making the step up after managing four birdies and two bogeys for a final-round two under 69.
Lee and Wilkinson will now join more than 150 golfers playing for 25 tour cards at the final stage of qualifying, a six-round tournament beginning on November 28 in California.
Alker and Geary both failed in their attempts to join their compatriots after finishing outside the top 19 at their respective second stage tournaments in California and Texas.
Hamilton professional Alker shot an even par 72 in the final round to miss the qualifying mark by just one shot, ruing a costly stretch on the front nine where he made three bogeys in succession.
Tauranga professional Josh Geary fell short of his PGA Tour dream, carding a one over par 73 to finish tied 59th and 12 shots off the qualifying mark.