"Hopefully, I will be a starter," said Davis, who threw 141 pitches. "As long as I can go five or six innings and give us a chance to win, I don't know why I wouldn't be starting.
"Johnny Oates showed a lot of confidence in me after throwing 125 pitches through eight innings to let me go and finish the game in the ninth."
Davis struggled early, allowing the first three hitters to reach base. Jose Offerman opened with a single, Bernard Gilkey was hit by a pitch, and Carl Everett singled to extend his hitting streak to seven games. With the bases loaded, Davis struck out Nomar Garciaparra.
"I was thinking strike him out or get a doubleplay," Davis said. "Just getting ahead of him is the key because, if you get behind, it's Nomar."
After the strikeout, Troy O'Leary grounded into a force at second and was almost doubled up, but first baseman Rafael Palmeiro couldn't handle the relay throw. Lou Merloni grounded out to end the scoring threat.
"We gave everything we had, it was just his night," Gilkey said. "Evidently, he did everything right."
Frank Catalanotto, 0-for-9 in the first three games of the series, gave the Rangers a 2-1 lead with a double in the fifth inning, and helped Texas avoid a sweep.
Boston dropped one game behind Oakland in the AL wild-card race. The Rangers won for only the third time in 11 games.
"We had lots of baserunners and lots of opportunities," Red Sox manager Jimy Williams said. "We just couldn't get those hit early."
Jeff Fassero (8-7) held the Rangers hitless until Palmeiro singled to lead off the fifth. Ricky Ledee and Royce Clayton followed with singles to load the bases, and Catalanotto hit a double. Scott Sheldon's sacrifice fly gave the Rangers a 3-1 lead.
In other games:
INDIANS 12, MARINERS 4
At Cleveland, Kenny Lofton homered twice and drove in a career-high six runs as the Indians handed Seattle its eighth consecutive loss.
The Mariners have allowed at least nine runs in the last seven losses - tying a 99-year-old major league record set by the New York Giants, Sept. 3 to 6, 1901. Seattle last lost eight straight during a club-record 14-game skid in September 1992.
ATHLETICS 5, TIGERS 4
At Detroit, a wild pitch by Nelson Cruz (4-1) allowed the tiebreaking run to score in the 11th inning as Oakland snapped the Tigers' six-game winning streak.
The win ended a seven-game road losing streak for the A's and moved them within two games of first-place Seattle in the AL West.
ANGELS 5, YANKEES 4
At New York, Kevin Stocker blooped a tiebreaking single and Anaheim, shut out on two hits for six innings by David Cone, broke loose against the Yanks' bullpen.
Tim Salmon hit a two-run homer and Adam Kennedy and Stocker had RBI singles as the Angels scored four times in the seventh against Mike Stanton, Jeff Nelson and Randy Choate for a 4-3 lead.
Matt Wise (2-1) gave up three runs in six innings. Shigetoshi Hasegawa pitched the ninth for his sixth save.
D-RAYS 12, WHITE SOX 11
At Chicago, Jason Tyner's RBI double in the ninth inning capped Tampa Bay's rally from a four-run deficit.
The Devil Rays, who led 6-2 before battling back from a 10-6 hole, tied the game at 11 when Bobby Smith led off the ninth inning against Keith Foulke (3-1) with his fourth homer. Foulke blew his fifth save in 27 chances.
BLUE JAYS 6, TWINS 3
At Toronto, David Wells became the first 18-game winner in the majors as the Blue Jays defeated Minnesota.
Wells (18-5) equaled his career high in wins - he was 18-4 in 1998 with the New York Yankees. The 18 wins are the most by a Blue Jays lefthander.
ORIOLES 2, ROYALS 1
At Baltimore, Sidney Ponson (7-8) allowed one run in eight innings and Jeff Conine doubled in the tiebreaking run in the eighth as the Orioles snapped Kansas City's four-game winning streak.
Melvin Mora, who scored both Baltimore runs, led off the eighth with a walk off Kris Wilson (0-1). After a sacrifice and an intentional walk to Albert Belle, Conine hit a drive to center that bounced over the wall.