ST. PETERSBURG, Fla. — David Price just became the October X-factor for the Red Sox.

In a dominating debut appearance Sunday as a Boston reliever – 21 pitches, two perfect innings, two strikeouts – Price altered the entire look, shape and feel of the bullpen as it gears up for the playoffs.

If he can replicate or even approach that type of effort in his remaining appearances over the final two weeks of the regular season, there will be no overstating the magnitude of the lift he would provide.

He is an elite pitcher when healthy, and in Sunday’s 3-2 loss to the Tampa Bay Rays, he made the sudden and unwanted transition from starter to reliever look easy. He threw four pitches – fastball, knuckle curve, cutter and change-up – and got outs with three of them.

His arrival does not suddenly elevate the Red Sox bullpen into the ranks of the Yankees and Indians, but maybe it’s time to start to imagine how good this bullpen can be.

Price, a Cy Young winner enduring a long, painful and emotionally challenging season because of the tear he has somewhere near his left elbow, could not have been less surprised with his success.

“Done this for a long time,” said Price. “My last bullpens, my last live (batting practices) were really good. That mound is still 60 feet, 6 inches away from home plate. I wasn’t surprised.”

John Farrell was, and very much so.

“That was even more than personally anticipated,” Farrel said. “From the power to the touch and feel, I’m amazed that someone can pitch – haven’t pitched in a game in seven weeks and come out with that kind of command and throw three, four pitches for strikes. He’s a unique pitcher, and that was really a strong two innings of work today.”

When Price debuted with the Rays in September 2008, he was coming off a full, healthy rookie season in the minors. He became an X-factor in Tampa Bay’s run to the World Series, something the Red Sox team he finished off in the American League Championship Series remembers well. He then returned to starting virtually uninterrupted – he made one relief appearance on the final day of the 2010 season – until this year, when his still-concerning elbow issue cropped up in spring training.

Eleven midseason starts were all the Red Sox got from him before the elbow started to bark again. It’s settled down enough that Price can step back on the mound, even if it’s a role he never sought.

“I knew I wanted to start, but I didn’t map it out in my head or anything,” said Price. “I’ll do whatever.”

Price pitched no differently than he did as a starter, rather than downgrading to the two-pitch arsenal most relievers rely upon. He threw all his pitches – nine fastballs and four apiece on the three off-speed pitches – and 15 of the 21 he threw for strikes.

The earliest Price would pitch again would be Wednesday in Baltimore, and he’ll get more chances after that. It will all be prep work for what happens with Price when the playoffs start.