Already guaranteed a PGA Tour card with an 18th-place finish on the Web.com Tour's regular-season money list, Murray closed with a 3-under 68 to beat Smith by a stroke in the third of four events in the Web.com Tour Finals. Tway tied for third with third-round leader Martin Flores.
Murray finished at 12-under 272 on Ohio State's Scarlet Course and earned $180,000 to jump from 11th to second with $407,963 on the PGA Tour priority list among the 25 card-earners from the Web.com money list. The former Wake Forest and Arizona State player will be 23 on Saturday.
Murray lost in a three-man playoff in August in the Web.com Tour event in Wichita, Kansas.
Smith also shot a 67. After finishing 157th in the PGA Tour's FedEx Cups standings, the Australian made $108,000 to go from 48th to third with $114,910 in the series race for 25 more PGA Tour cards.
Tway had a 67 to match Flores (74) at 10 under. Tway was 27th on the Web.com money list. His $58,000 check moved him from 52nd to ninth with $63,975, more than enough to secure one of the 25 cards. The last PGA Tour card went at $33,650 in 2013, $36,312 in 2014 and $32,206 last year.
Flores earned a card with a fifth-place finish on the Web.com money list. He's fifth on PGA Tour priority list with $346,313, with regular-season money counting in the total.