Porcello (11-4, 3.12 ERA) has thrown 25 consecutive scoreless innings for Detroit, while Price (7-7, 3.50) leads the majors with 153 strikeouts.
Porcello, who can tie the New York Yankees' Masahiro Tanaka for the major league lead in victories, had never thrown a shutout until doing so in back-to-back outings, including a four-hitter in Tuesday's 3-0 home victory over Oakland.
"I don't want to jinx it," he said. "All I know is that I'm throwing the ball really well right now, I'm making consistent pitches when I need them, and my defense is helping me out. I'm also getting some good breaks, which every pitcher needs."
On Tuesday, the right-hander became the first in franchise history to throw a shutout without walking or striking out a batter since Dizzy Trout in 1944. He's the first Tigers pitcher to throw consecutive shutouts since Jack Morris had three straight in 1986.
"Obviously, Rick is throwing the ball extremely well right now," manager Brad Ausmus said.
The same can be said about Price, who seeks his first three-start win streak of 2014. His run of striking out at least 10 in five straight outings ended Tuesday as he finished with nine and allowed one run in seven innings in a 2-1 road victory over the Yankees.
Price, who could have joined Nolan Ryan, Randy Johnson and Pedro Martinez as the only pitchers to strike out at least 10 in six straight starts, insisted trade rumors aren't concerning him.
"I just play ball," he said. "That's my job."
The left-hander has limited Miguel Cabrera to one hit in 14 at-bats with six strikeouts, making him the only pitcher Cabrera has faced that many times not to surrender more than one hit.
Victor Martinez has presented more of a challenge with eight hits in 17 at-bats against Price, who is 4-1 with a 2.41 ERA in five starts against the Tigers (48-36).
Martinez, however, did not start for the fourth time in six games Saturday due to soreness in his left side.
"If push comes to shove, we could probably keep him down all the way through the All-Star break," Ausmus told MLB's official website. "But right now, we're just going to see how he feels every day."
Porcello is 2-2 with a 2.73 ERA in five starts against Tampa Bay (40-50), limiting Matt Joyce, Evan Longoria and Ben Zobrist to three hits in 24 at-bats.
He has never faced Kevin Kiermaier, who went 3 for 4 with two triples and three RBIs in Saturday's 7-2 victory for Tampa Bay. Kiermaier ended a stretch of 15 at-bats without a hit as the Rays won for the seventh time in eight games.
"I really like the way we're swinging the bats right now," Kiermaier said. "Everyone's doing their part, and we're all staying positive and we're having so much fun out there on the field."