A recount showed Romney, a former Massachusetts governor, captured 2,269 votes to 2030 for Paul, the Texas congressman, CNN reported.
Former Sen. Rick Santorum of Pennsylvania received 1,052 votes and former House Speaker Newt Gingrich, 391. Neither Santorum nor Gingrich actively competed in the Maine caucus.
Earlier, Maine Republican Party Chairman Charlie Webster had conceded the state party made clerical errors counting caucus results but said they hadn't affected the outcome.
Among other errors, Webster said, e-mails reporting vote totals went to spam in an e-mail account, Politico reported.
Webster Saturday declared Romney the winner in Maine's Presidential Preference Poll by fewer than 200 votes, but all municipalities had not yet reported results.
"There were clerical errors that did not significantly change the numbers," Webster told Politico. "There were several smaller towns that were left out, the reporting was wrong. … We've corrected those clerical errors and will send those numbers out [soon]."
In Portland, the state party's results had originally indicated Paul won by 15 votes when Romney actually won by 15, Webster said.
Webster also said "about a half a dozen" towns were never added to the tally election night and in a few cases, e-mails from municipalities reporting caucus results "went to spam" in the state party's e-mail system.