PAWTUCKET — When it came time to decide on a closer for his team this season, Pawtucket manager Ron Johnson had several options.

His roster includes Dan Kolb, a veteran of four major-league teams. Kolb has 73 big-league saves and was a National League All-Star with Milwaukee four years ago. The PawSox also have Craig Hansen, Boston’s hard-throwing first-round draft choice three years ago, one of the organization’s highly valued prospects.

One week into the season, though, neither of those guys is doing the job.

Instead, the pitcher finishing games — and doing it beautifully — is a little-known seven-year minor-league veteran who came into pro ball as an undrafted free agent.

Lee Gronkiewicz, all 5-foot-11 and 180 pounds of him, picked up save number two yesterday. He could not have been more efficient as he threw seven pitches, all strikes, in a scoreless ninth that ensured a 4-1 victory over the Lehigh Valley IronPigs at McCoy. Gronkiewicz has not allowed a run in three appearances.

As would be expected from a player who has spent a grand total of eight days in the majors, his December signing drew very little attention. Gronkiewicz, out of the University of South Carolina, had spent seven years in the Cleveland and Toronto organizations. That he was not drafted is not a surprise. He does not fit the profile scouts look for, especially in a closer.

Gronkiewicz not only is small physically, as closers go, he does not throw overly hard.

“I throw 86 to 88, have a cutter, a curve ball and a split,” he said. “That’s it. I try to throw strikes, not walk people.” He is here because of Boston pitching coach John Farrell.

“They called my agent, offered me a contract and I accepted it,” said the unassuming, straight-talking Gronkiewicz. “John was the minor-league coordinator with the Indians when I came up with them. He was well aware of me. He liked my demeanor. That’s why they wanted me.”

While Gronkiewicz might not look like a closer, but his numbers do. Working his way up from the bottom, he has compiled a 2.25 ERA in 335 games, all but one in relief. He has 154 saves. Last season, splitting his time between Double-A New Hampshire and Triple-A Syracuse, he had an awesome 8:1 strikeout/walk ratio — 83 strikeouts, 10 walks.

He was called up by the Blue Jays in June and spent eight days in the bigs. In his only appearance, he went four innings against the Dodgers on June 19, allowing two hits and one run. Gronkiewicz said he is not even aware of his numbers from last season.

“Numbers are just numbers. I let you guys worry about those,” he said. “I just try to throw strikes and not walk people.”

More heralded pitchers who put together numbers like he has compiled likely would have spent far more than eight days in the majors.

Gronkiewicz is not locked into the closer role. For example, Hansen will work multiple innings in many of his outings as the Sox get him work.

“If I bring him on in the eighth, he probably would stay in and pitch the ninth, too,” Johnson said. Kolb also is ready if asked. But Gronkiewicz has the job for now.

“I don’t think we have anything etched in stone,” Johnson said. “But he has a history of doing the job and being able to handle it.”

Gronkiewicz is happy to be with the Boston organization.

“It’s been great. You can tell they have a championship organization,” he said. “It shows from the top all the way down in how they treat their players. The first day we had a meeting with Theo [Epstein] and he said I’m a Red Sox now. That’s what I believe.

“I signed as a free agent. Most guys who sign as a free agent when they’re 22 don’t get to where I’m at now. I just go out there and try to continue to have success,” Gronkiewicz said. “I got a chance at the big-league level. Hopefully I’ll get another.”

pkenyon@projo.com