Davis has managed homers in six successive games now, with his decisive contribution against the Rays coming in the fourth inning.
It kept the Orioles on the heels of the New York Yankees, trailing by one game going into Wednesday's determining fixtures.
The Yankees were pushed close by the Boston Red Sox in New York, with Raul Ibanez making the key contributions, firstly with a homer in the ninth inning and then when singling in the winning run in the 12th.
There would be a tie-breaker on Thursday to settle the division if New York were to lose on Wednesday and Baltimore win. They face the same opponents as in this penultimate round. Boston have now lost seven straight.
There will be no need for an additional match on Thursday to decide who tops the AL West.
The Oakland Athletics moved level with the Texas Rangers by beating their divisional rivals 3-1 to set up a final-night decider between the teams for first place.
The Detroit Tigers already had the AL Central title in the bag, so a 4-2 loss against the Kansas City Royals was far from ruinous.
Miguel Cabrera drove in two runs early for Detroit before the Royals, who had homers from Alcides Escobar and Jeff Francoeur, took control.
The Chicago White Sox, who cannot reach the post-season but will finish as divisional runners-up to Detroit, were edged out 4-3 in Cleveland by the Indians after 12 innings.
Jason Donald had an RBI single before Chris Seddon kept Chicago scoreless at the bottom of the 12th.
Kelly Johnson had a two-run homer for the Toronto Blue Jays in a 4-3 win over the Minnesota Twins, while the Seattle Mariners crushed the Los Angeles Angels 6-1.
In the National League, the St Louis Cardinals secured a wild card match against the Atlanta Braves on Friday after a tense wait.
The Cardinals lost 3-1 at home against the Cincinnati Reds, for whom Scott Rolen hit a home run, and that kept their post-season hopes in the balance.
They knew a win for the Los Angeles Dodgers in the late match against the San Francisco Giants would take the race down to the final night.
But it was not to be for the Dodgers, who would still have needed a turnaround in Wednesday night's games, as they lost 4-3 to the Giants.
An under-strength Atlanta line-up lost 5-1 to the Pittsburgh Pirates, with Garrett Jones homering for the victorious home side. Atlanta, runners-up to Washington in their division, knew they had the wild-card game to ready themselves for so rested key players.
Washington's NL East title-winning party fever spilled over into their latest clash with the Philadelphia Phillies as Adam LaRoche cracked his 33rd homer of the season to reach 100 RBIs for the season in the Nationals' 4-2 victory.
The Florida Marlins beat the New York Mets 4-3 in an 11th inning, while the Milwaukee Brewers won by the same score against the San Diego Padres, albeit in regulation. Martin Maldonado defined that contest with a grand slam in the fourth inning.
The Houston Astros, with the worst record in the major leagues, were 3-0 winners against the Chicago Cubs, the team with the second-worst performance this season.
Aaron Hill's three-run homer in the ninth inning turned a deficit into a match-winning score as the Arizona Diamondbacks saw off the Colorado Rockies 5-3.