Hungary remained in third place on 16 after losing 4-3 in Greece and will try to reach the finals via the playoffs.
Constantin Budescu, who replaced the ineffective Claudio Keseru in Romania’s starting lineup, scored twice before the break and almost grabbed a hat-trick in the second half.
Alexandru Maxim put the result beyond doubt with their third goal eight minutes from time.
"It was a difficult campaign but we expected that because it was a balanced group," said manager Anghel Iordanescu. "We deserve to qualify.
"We’re very happy though I wanted to secure qualification against Finland in Bucharest (on Thursday) because I wanted to share the joy with our fans," he added.
"It is a success Romanian football was looking for. Our guys played really well from a tactical point of view. We should have qualified earlier, not to keep our supporters under pressure."
GREAT START
Iordanescu’s side could not have wished for a better start, going ahead thanks to Budescu’s first international goal after a well-worked free kick in the fourth minute.
Budescu then scored an astonishing goal from a seemingly impossible angle on the right touchline with his shot looping over goalkeeper Gunnar Nielsen on the stroke of halftime.
Budescu’s strike revived memories of former great Gheorghe Hagi’s amazing goal against Colombia at the 1994 World Cup when Romania, under Iordanescu, reached the quarter-finals for their biggest achievement.
Maxim wrapped up the victory when he played a one-two with Bogdan Stancu before sliding the ball into the net.
Romania, criticised by some pundits for their defensive approach, conceded only two goals in the campaign, fewer than any of the 53 teams in the qualifying competition in Europe.
"I think the boys deserve congratulations for what they’ve done throughout the whole campaign and I don’t want to miss (former coach) Victor Piturca, who has made a huge contribution, Iordanescu said.
The coach, who guided Romania to Euro 96 and the 1998 World Cup, began his third spell in charge last October, replacing Piturca who quit after agreeing to join Saudi Arabia's Al Ittihad on a lucrative contract.
(Reporting by Angel Krasimirov; Editing by Ken Ferris)
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