An Elections Canada review had already indicated Penashue overspent his legal limit by almost $4,000.
Penashue's former campaign manager Reginald Bowers later apologized to Elections Canada for mistakes and missing paperwork.
But CBC News cites new documents from Penashue's Elections Canada file that an airline in Labrador wrote off all but $7,000 of a nearly $25,000 travel bill.
Rae took aim Wednesday at Penashue in the House of Commons during question period.
"There's substantial evidence now that there has been overspending in the last election by the member from Labrador, the minister for intergovernmental affairs, by over $20,000," Rae said of a campaign that had a legal limit of just under $84,500.
"This is not simply a question about Elections Canada, Mr. Speaker. This is a question about what are the standards of the prime minister of Canada with respect to the conduct of his candidates? Instead of buying elections, why not a byelection, Mr. Speaker?"
Corporate freebies are outlawed under election rules brought in by the Conservatives. Alternately, if the allegations are true and Penashue had paid the full airline bill, he would have spent several thousand dollars over his legal campaign limit.
"As has been conceded some time ago, there were errors in the filings of the official agent in this case," Prime Minister Stephen Harper replied over heckles from the opposition benches.
"That is the individual responsible. A new official agent was named. That agent has been working for some time with Elections Canada to correct these problems."
Following question period Jack Harris, the NDP MP for St. John's East, told reporters his party wanted more of an explanation.
"Mr. Penashue has the right to explain himself. Where is he today? He’s not here in the House. He’s not explaining himself. He’s leaving it to others. That’s irresponsible."
Bowers apologized to Elections Canada in a letter dated last May 25.
"You must keep in mind, this was my first time being an official agent and campaign manager so I had to get advice wherever I could and very quickly because I had very limited time," he wrote to the office of the chief electoral officer. "So mistakes were made.
"I apologize for this and will advise differently the next time if I am involved. But this time, given the circumstances, record keeping and budgeting did not get the top priority."
CBC reports that a letter from the lawyer for Provincial Airlines, sent to Elections Canada, says the company wrote off anything over $7,000 in the fall of 2011 — more than four months after the election — when Penashue's campaign team said it could not pay more.
Penashue won an upset victory over Liberal incumbent Todd Russell by just 79 votes in the sprawling Labrador riding. He repeatedly referred to his extensive travels in the region during his campaign.
Bowers went on to be named by the federal government last December to the federal-provincial board that regulates Newfoundland's offshore oil sector.
Elections Canada does not discuss specific cases and Penashue was not available for an interview.
In an email, his spokesman Cory Hann said: "We are continuing to work with Elections Canada to make any amendments that might be needed."