The Oaks trailed 15-0 early in the second half after Canada had scored tries either side of the break through wingers DTH Van Der Merwe -- his fourth in as many matches at the World Cup -- and Jeff Hassler.
Romania, however, made the most of their pronounced forward superiority and stormed back with converted scores from captain and number eight Mihai Macovei in the 53rd and 74th minutes to get within a point.
Canada were down to 14 men after flanker Jebb Sinclair was sin-binned and the Romanian pack smashed the Canucks at yet another scrum to earn a penalty and give Vlaicu his chance of glory from 35 metres out.
The 29-year-old centre, who also converted both tries, made no mistake with a curling effort to earn his side their first victory in Pool D and condemn Canada to only a second winless tournament in eight World Cup appearances.
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"I never give up," Romania's Welsh coach Lynn Howells told reporters.
"We said if we could stay within 14 points going into the last 20 minutes we could start playing the sort of rugby we wanted.
"The disappointing thing was that we played so poorly in the first half, that was really unacceptable."
The Oaks have one final match against Italy in Exeter on Oct. 11 and could still finish third in the group with a victory to qualify for the 2019 World Cup.
The Canadians will rue being unable to make the most of the string of scoring chances in the first half and the inaccuracy with the boot of scrumhalf Gordon McRorie, who missed two penalties and a conversion.
"Pretty disappointing from our point view, 15-0 up, played all the rugby in the first half but didn't score enough points," Canada coach Kieran Crowley said.
"Romania deserved their win, got their maul together, got their scrum together and scored the points."
Canada had looked to be on their way to victory, however, when Van Der Merwe squeezed between two defenders and reached over the line to touch down, becoming the first player from a tier two nation to score tries in four successive matches at a World Cup.
Only Wales and British and Irish Lions flyer Shane Williams had previously scored a try in all four of his country's World Cup pool matches, achieving the feat in 2007.
They had failed to exploit a 20th-minute yellow card for Catalin Fercu after the Romania fullback took out Canada centre Nick Blevins in the air.
Canada got a second try four minutes after the break through Hassler but then, in the words of their coach, "the wheels came off".
The Romanian pack finally got the catch-and-drive going to send Macovei over the try line 13 minutes into the half and camped on the Canadian line for a good 10 minutes before the captain crashed over in a pile of bodies for his second.
"It's important for me and my team mates to believe in ourselves or there is no place for us on the field," Macovei said.
"We must believe right until the last second, even against the big nations, that is what our coach has taught us."
(Editing by Ed Osmond)
