"Really commanding performance," Rays manager Joe Maddon said of Price. "The best game I've seen fastball command out of him."
Price (4-3) is undefeated against the Blue Jays, winning eight times in nine starts. The left-hander allowed four hits and struck out 10 over 8 2/3 innings.
"He was strong," Toronto manager John Farrell said. "He kept his velocity throughout the eight-plus innings he was there. I thought he had a lot of strikes on the inside part of the plate. Caught a number of guys looking. Obviously he's had a lot of success against us, and again that was the case today."
Damon had two hits, which moved him past Steve Garvey (2,599) into 75th place on the career list. His fifth-inning double (490) tied him for 59th place with Mickey Vernon on that list.
The Rays took two of three from the Blue Jays and won their 12th consecutive home series over Toronto, since July 30 to Aug. 1, 2007. Tampa Bay has won eight of its last 11 overall.
Price was pulled by Maddon with two outs and nobody on base in the ninth, prompting boos, after Patterson hit an RBI grounder. John McDonald reached second to start the inning on a throwing error by shortstop Sean Rodriguez.
Maddon was concerned about Price's pitch count, which had reached 118 for the game.
Kyle Farnsworth got the final out after allowing a single to Escobar for his sixth save.
Adam Lind extended his hitting streak to 10 games with an infield single off Price during the seventh, but it wasn't enough to help Toronto avoid its fourth loss in five games.
John Jaso had an RBI double, Damon drove in a run with an infield single and Matt Joyce hit a sacrifice fly off Kyle Drabek (2-2) to put the Rays ahead 3-0 in the third. Joyce has eight RBIs over his last seven games.
"He's a great pitcher," Drabek said of Price. "He did a good job today."
Drabek had his start moved up one day to replace Ricky Romero, who was scratched with a mild left oblique strain. The right-hander gave up three runs and six hits in 5 2/3 innings.
Romero is scheduled to pitch Saturday against the Detroit Tigers. The left-hander had a long-toss session and threw at 60 feet on flat ground.
Blue Jays slugger Jose Bautista, who missed his third straight games with neck spasms, continues to improve and remains on target to resume swinging a bat Friday. He could return to the lineup Sunday.
Maddon said right-hander Jeff Niemann (back) is expected to go on the DL after an MRI exam. He left his start Wednesday night after four innings. ... Toronto second baseman Aaron Hill (strained right hamstring) was sent to Class A Dunedin for a rehab assignment. ... Rays center fielder B.J. Upton, ejected after striking out in the ninth Wednesday, had not heard before the game about any punishments from MLB officials. He slammed his bat and helmet to the ground after being thrown out by umpire Chad Fairchild. ... Maddon, also ejected Wednesday, said postgame the Rays still had not been contacted by baseball officials about the matter. ... Rays infielder Felipe Lopez accepted an assignment with Triple-A Durham. He was designated for assignment on Tuesday.