Luck was 2-under and inside the top 15 through 12 holes at the Ohio State University Scarlet Course but his stumbling finish saw him drop to T39 at day’s end.
While not fatal, it is a finish the 2016 US Amateur champion will be unhappy with as he chases a card on the PGA Tour over the next month.
The four-tournament Finals series, which brings together both PGA Tour and Web.com Tour players, will hand out 25 cards after the Tour Championship on October 1.
To be among those to graduate, Luck will need to be one of the top 25 earners on a mini money list covering only these four events, every dollar earned crucial to both getting into the 25 then finishing as high up as possible.
The 21-year-old West Australian is one of this country’s most promising prospects of recent times and has already proved he has the game to compete at the top level with a T5th finish at the PGA Tour's Quicken Loans National in July.
Luck is one of eight Australians eligible for the Finals, Scott Hend and Brett Drewitt leading the way through 18 holes at 1-under and T25.
Drewitt graduated through this process last year but failed to finish inside the top 125 in the FedEx Cup standings and retain his privileges.
Hend, who lives in Florida and played one season on the US circuit in 2006, performed well enough at last month's WGC Bridgestone Invitational to earn his way into the series.
A full-time member of the European Tour and last year's Asian Tour Order of Merit winner, the long hitting 43-year-old has made no secret of the fact he would like to return to the US Tour and feels his game is good enough to compete and win there.
Cameron Percy, Rhein Gibson and Jamie Arnold are next best of the Australians at 1-over and T55 while both Matt Jones and Stuart Appleby limped to 4-over rounds of 75 to be T106 and in danger of missing he cut.
American Keith Mitchell leads the tournament courtesy of a 6-under 65, Mexico’s Abraham Ancer is outright second a stroke further back.
Sam Saunders and Alex Cejka share third at 4-under ahead of a group of 10 players at 3-under and T5.