Reese fired a 6-under 66 and joined Meshiai atop the leaderboard at 19-under-par 341. R.W. Eaks posted a 3-under 69 on Sunday and is one shot back at The King & The Bear course.
After Monday's final round, 15 playing cards for the 2005 Champions Tour season will be issued. Seven players will get full status for next year, while eight receive conditional status.
Meshiai, a 50-year-old from Japan, got off to a slow start with a bogey at the first. He recovered with three consecutive birdies from the third, but dropped another stroke to par at the sixth.
Meshiai closed his front nine with birdies at seven and nine to get to 19 under par. That would be it for scoring for Meshiai as he parred his entire back nine to get into position to win Q-School.
Reese birdied the first, then bogeyed No. 4. He atoned for the miscue at four with three birdies in a row from the fifth to make the turn at 3-under-par 33.
Reese tallied birdies at 13, 15 and 18 and now is in good shape to earn his playing privileges for the elder circuit in 2005.
Brad Bryant (67) and Mark Johnson (70) are tied for fourth place at 17-under-par 343. Pat McGowan carded a 5-under 67 on Sunday and is alone in sixth at minus-16.
Ireland's Des Smyth (68), Norm Jarvis (68), former Champions Tour player Dick Mast (70) and Mike Malaska (70) are knotted in seventh place at 15-under-par 345.
Jim Ahern and Dave Barr, both of whom won in 2003, are on the outside looking in for their cards next year. Ahern shot a fifth-round, even-par 72 and is part of a group tied for 21st at minus-11. Barr managed a 1-over 73 on Sunday and is tied for 36th at 6-under-par 354.
Stewart Ginn, who won the 2002 Senior Players Championship, posted an even-par 72 and is tied for 40th at 5-under-par 355.
Former Major League pitcher Rick Rhoden will be back to the Celebrity Tour in 2005. He struggled to a fifth-round, 6-over-par 78 and is one shot out of last place at plus-5.