The New Zealand fighter failed to impress against the Romanian who took the bout at two weeks' notice, winning a 119-108 117-110 117-110 decision.
The champion landed sporadic flurries throughout but never looked like scoring a stoppage in Auckland.
He has said he will campaign overseas, with Britain's WBA and IBF champion Anthony Joshua a potential opponent.
Though he remains unbeaten in 23 fights, the manner of this win may make Parker a tougher sell for pay-per-view audiences overseas.
The 25-year-old - who claimed the vacant WBO belt against Andy Ruiz in December - did land some shots when in close to Cojanu but when at distance he looked incapable of finding ways to rock a man three inches taller and around two stone heavier.
Cojanu, who now has 16 wins and three losses to his name, was one of Parker's sparring partners but stepped in to the main event when Britain's Hughie Fury withdrew through injury.
Cojanu landed a left hook of his own in the 10th round and chased a stoppage win in the 12th. But, in truth, he always looked occupied with spoiling Parker's work, most notably when having a point deducted for leaning on the champion's neck in the fourth.
Parker said afterwards: "You can all see why we bring Razvan into camp for us. He put on a great fight.
"I've done my best to keep fights here in New Zealand but it's down to us to go and get some exposure overseas now."

In 2014, a report by the public protector said Mr Zuma had "benefited unduly" from the upgrades.
Mr Zuma said the auditor-general and finance minister should determine how much he should repay to end the dispute.
The announcement comes a week before a constitutional hearing on the matter.
Africa Live: BBC news updates
How President Zuma's Nkandla home has grown
The refurbishment of the residence in the village of Nkandla, in Mr Zuma's home province of KwaZulu-Natal, has turned into a major political controversy in South Africa.
Some of of the money was spent on building an amphitheatre, swimming pool, and cattle enclosure.
The opposition Democratic Alliance (DA) and Julius Malema's Economic Freedom Fighters (EFF), who have called for a corruption investigation, say they are pressing ahead with their court case regardless of the president's latest offer.
Following Mr Zuma's announcement #PayBackThemoney is trending in South Africa - this was the phrase EFF MPs chanted at the president in parliament last year.
Many commentators seem sceptical.
Analysis: Milton Nkosi, BBC News
President Jacob Zuma's delayed willingness to pay back the money spent on the upgrades to his Nkandla residence could be a calculated move to avoid embarrassment at the Constitutional Court hearing expected next week.
But it could also be linked to the forthcoming local government election.
The Nkandla scandal has been a sore point for the governing African National Congress (ANC) which President Zuma leads, especially as the party faithful go out to campaign for votes.
Political analyst Professor Somadoda Fikeni told me that it could also be related to the president being "politically vulnerable as he enters his 'lame-duck' period and following his mis-appointment of finance ministers" at the end of last year.
Another consideration could well be an attempt to avert another episode of the chaotic scenes we saw during the opening of parliament last year when Julius Malema's Economic Freedom Fighters (EFF) heckled and disrupted the president's state of the nation address.
Security personnel had to be called into the chamber to remove the MPs who would not stop shouting "pay back the money'" while President Zuma desperately tried to deliver his speech.
Punches at South Africa parliament
Why did Zuma sack two finance ministers in a week?
All figures in 2013 financial terms
Source: Public protector report
Joseph Parker defended his WBO heavyweight title for the first time in a drab points win over Razvan Cojanu.
[NEXT_CONCEPT]
South Africa's President Jacob Zuma has agreed to repay some of the $23m (£15m) the government controversially spent on upgrading his private rural home.