Romania's rolling maul finally kicked into gear, resulting in a try from replacement left winger Adrian Apostol, who took a feed from No. 8 Daniel Carpo and dotted over.
That made it 29-10 with 13 minutes remaining and, just to be safe, Allan took a penalty kick in front of the posts, drawing some jeers from the try-hungry crowd at Sandy Park who wanted Italy to run the ball.
But there was more at stake than entertainment value, and the Italians were right to be cautious in light of Romania's fine flourish.
Lock Valentin Poparlan barged his way over for a try he was not even aware he had scored, until it was awarded following one of several television referrals that stalled an otherwise flowing game.
Then, with one minute remaining, Apostol capped off a sweeping move with another try down the left, prompting a jubilant reaction from him, and an even bigger one from coach Lynn Howells.
But it was too late.
Italy finished behind Six Nations rivals Ireland and France - who played their pool decider late Sunday - and Romania ended in fourth spot.
In a one-sided first half, Italy had two more tries ruled out for knock-ons.
If Romania had only started the tournament the way it finished, perhaps Howell's teams would be booking tickets in 2019 to Tokyo.
Match stats
Chalkboard
Action areas
