ARLINGTON, Texas ? If the third exhibition game is the one that most closely approximates the regular season, the 49ers have a lot of work to do before their Sept.13 opening.

The 49ers? first-team offense managed just three points with starting quarterback Shaun Hill at the controls for the first five possessions. When the starting unit exited after one series in the second half, the 49ers got things into gear.

Rookie quarterback Nate Davis solidified a spot on the 49ers? 53-man roster with an impressive showing to lead the 49ers to a 20-13 exhibition victory over the Dallas Cowboys on Saturday night.

With less than four minutes remaining, coach Mike Singletary opted to tie the game with an Alex Romero field goal, rather than go for it on fourth-and-1 from the 6-yard line. It was a unique decision ? the kind not often seen in a game that has no bearing in the standings.

?It has no meaning for you,? said Singletary, whose team improved to 3-0 in the exhibition season. ?Every game we play has meaning to me. I would never enter a game thinking that it doesn?t matter.?

And the final couple of minutes certainly had meaning for Davis and undrafted rookie running back Kory Sheets.

Davis led the 49ers? on a 91-yard scoring sprint that lasted a mere 79 seconds. Sheets provided the winning margin on a 9-yard touchdown on a power run up the middle with :33 remaining.

?It?s starting to click,? Davis said. ?I?m starting to pick up that confidence.?

Davis, a fifth-round draft pick from Ball State, completed 10 of 15 passes for 132 yards. It seems unfathomable at this point that Davis will not have a spot on the 49ers? 53-man roster when the 49ers open the season. He is likely battling veteran Damon Huard for the No. 3 job.

?I think Nate did a fine job,? Singletary said. ?I don?t know who?s on the other side of the ball (for the Cowboys), but they are professionals.?

Sheets led the 49ers with 42 yards and two touchdowns on 11 carries. Known for his lightning speed, the 208-pound Sheets also showed surprising power to get into the end zone in the final minute for the winning points.

?The offensive line did a great job of getting me deep before anybody touched me,? Sheets said. ?Once I get a full head of steam, it?s tough to tackle me.?

The 49ers? first-team offense was not nearly as impressive. Not even the massive high-definition video board that hovers 90 feet above the playing field at the gleaming new stadium could make the 49ers? offense look good.

?I would have liked for it to have gone a bit smoother than it did,? Hill said. ?I don?t know. You can?t tell a whole lot right now. I just wish we could have put a few more points on the board.

?I don?t think there?s any reason for panic, that?s for sure. The offense is coming together.?

Hill played the first half and the first possession of the third quarter. He completed 9 of 17 pass attempts for 79 yards. The most success he enjoyed came was with receiver Arnaz Battle, who caught three third-down passes for 41 yards.

Hill was named the starter on Monday over Alex Smith, who did not suit up due to a thumb sprain. Hill said this next week will be crucial in gaining timing and rhythm with the offense. With two-a-day practices concluded, the receivers will have fresh legs and able to run at top speed, he said.

The 49ers managed just 102 yards of total offense in the first half. Frank Gore rushed for 19 yards on five carries before Singletary told him to take off the remainder of the night.

?Even though I wanted to do more, I felt really good in the game,? Gore said. ?I was happy to be out there, especially against the Cowboys who are supposed to be a top-tier team. On some of the runs, we made a few mistakes, but we?ll watch the film and we?ll correct that. And when we correct it, it?s going to be crazy.?

Linebacker Patrick Willis saw his first action of the exhibition season after missing two games with an ankle/Achilles injury. Willis recorded four tackles while playing approximately 40 snaps.

?Everything was moving 100 miles per hour. It was crazy. Whoever said that not playing in the preseason doesn?t affect them, that?s not true at all. I still feel like I need to play in the preseason. I?m glad I was able to play this preseason.?

For more on the 49ers, go to Instant 49ers at http://blog.pressdemocrat.com/49ers. You can reach Staff Writer Matt Maiocco at matt.maiocco@pressdemocrat.com