Price (19-6) scattered six hits over eight innings and allowed only one runner past second base. He struck out eight and walked none in what likely will be his final start of the regular season.
The Rays entered Tuesday with a one-half game lead over the New York Yankees in the AL East.
Carl Crawford and Carlos Pena hit solo homers to support the 25-year-old left-hander before a crowd of 17,891 that joined in the celebration at Tropicana Field.
Dan Johnson and Ben Zobrist also drove in runs off Orioles starter Brad Bergensen (8-11).
The Rays made an improbable run to the World Series two years ago with Price coming out of the bullpen to close out their pennant-clinching win over Boston.
Price took the mound one night after he and All-Star third baseman Evan Longoria made comments critical of the announced crowd – 12,446 – for a potential clincher on Monday. Longoria called the turnout "disheartening," while Price weighed in on Twitter, calling it "embarrassing."
Team president Matt Silverman announced before the game that the Rays will make available 20,000 free tickets for Wednesday night's regular-season home finale against the Orioles, a decision the executive said probably wouldn't have been made if the players had not spoken out about low attendance.
Any fans who purchased tickets in sections where free ones are located may exchange them for a lower box seat.
"This is about getting more energy into Tropicana Field, getting this place packed, and for the players to thrive off of that emotion," Silverman said. "We saw it in the past. We've seen it this year, and we will see it in the postseason."
Price, who this season became the youngest pitcher to start an All-Star game since Dwight Gooden in 1988, didn't allow a baserunner past second base until the seventh inning. He struck out Nick Markakis to finish a one-two-three eighth, and Rafael Soriano worked a perfect ninth in a non-save situation.
B.J. Upton's RBI single in the second inning gave Price all the offensive support he would need. Johnson had a run-scoring double in the third, and Pena's 28th homer made it 3-0 in the fourth.
Pena entered Tuesday batting .198, lowest among all major league qualifiers, and he hadn't homered since going deep against the Yankees' Ivan Nova on Sept. 14. Crawford hit his 17th homer after Zobrist hit a sacrifice fly earlier in the fifth.
Bergensen allowed five runs and six hits over five innings.
Notes
Longoria, out of the lineup for the fifth consecutive game, remains day to day with strained left quadriceps. … Orioles 2B Brian Roberts was a late scratch because he's wasn't feeling well. He was replaced by Julio Lugo. … Baltimore manager Buck Showalter, team president Andy MacPhail and major league scout Bruce Kison were among a group that looked at the renovations taking place at the Orioles' spring training complex in nearby Sarasota. Showalter called the changes "impressive."