"He does not lack for confidence," Rays manager Joe Maddon said. "He really wanted to be in that moment."
Desmond Jennings drew a leadoff walk in the 10th from Jean Machi (2-1) and stole second. Ben Zobrist was intentionally walked and Evan Longoria walked to load the bases on four pitches before Myers won it on his 0-1 liner that went over the left fielder's head.
"It was just one of those things that I knew he had to throw a good pitch," Myers said. "It's a good situation to be in, bases loaded, no outs. I just tried to stay calm up there."
Myers' parents were in attendance for his first walko-ff hit. He had a 12-game hitting streak end Friday.
"It's pretty cool to have them here for this one," Myers said.
Closer Fernando Rodney (4-2) allowed two hits during a scoreless 10th, striking out Brandon Crawford with two on and two out.
The starters were outstanding.
Price gave up one run, five hits and struck out five in nine innings. In seven starts since returning from a left triceps injury, the Rays left-hander has allowed just 10 runs, 38 hits, one walk, and struck out 40 over 57 1-3 innings.
"It's just executing pitches," Price said.
Lincecum allowed one run, six hits, one walk and fanned five in seven innings.
"We know we were up against some good pitching and we knew we had to make something happen, but you don't go out there thinking `I've got to pitch against Price, I've got to be perfect,'" Lincecum said. "I have to be perfect regardless of who I'm pitching against so it wasn't any added pressure."
Lincecum was making his third start -- the previous two were losses -- since throwing a no-hitter at San Diego July 13.
"He's in a good place," Giants manager Bruce Bochy said. "He's strong, he's got a lot of confidence going. He's using all his pitches. He's on the top of his game so it was a well pitched game on both sides."
It was just the second game in Rays history that featured two former Cy Young Award winners. The first came May 9 when Price pitched against Toronto knuckleballer R.A. Dickey in a contest that included both reigning winners.
Jeff Francoeur doubled leading off eighth for his third hit in three at-bats against Price and advanced to third on fly, but was left stranded when Crawford hit a soft liner and Andres Torres had a grounder.
Crawford put San Francisco up 1-0 with an RBI single in the third. Price struck out Crawford with runners on second and third to end the fifth.
Zobrist tied it at 1 in the third on a run-scoring grounder that drove in Jose Molina, who walked to open the inning. Molina went to second on wild pitch and advanced to third on Kelly Johnson's infield single that saw Lincecum get in the way of first baseman Brett Pill as he tried to tag out Johnson.
"We just got kind of tangled up over there," Lincecum said. "I can see that he wanted to cover first on his own, and I was just kind of in the way of that."
Giants catcher Buster Posey made a nifty play in the fourth on Myers' infield single. He chased down an errant throw by the first-base dugout and threw out the speedy rookie as he tried to reach second.
Longoria went 0 for 3, including three strikeouts and two walks, and is hitless in his last 17 at-bats. He hit just .194 in July, a month the Rays went 21-5.
NOTES: Rays RHP Alex Cobb, hit in the head by a liner in June, gave up one run and three hits over four innings for Class A Charlotte in his second rehab start. His first outing July 23 ended after just two pitches due to a blister. ... Giants RHP Ryan Vogelsong (fractured right hand) will make his fourth appearance with Double-A Richmond Sunday and is nearing a return to the rotation. ... Left-handed hitting Giants 1B Brandon Belt, who had three hits in Friday night 4-1 win after three games off for a mental break and work on his swing, was not in the lineup with Price starting.