Victor Piturca's men finished second in Group D with 19 points, nine points behind unbeaten Netherlands who ended Turkey's hopes of making the playoffs with a 2-0 win in Istanbul.
Romania, who have not reached the World Cup finals since 1998, missed a golden opportunity to open the scoring midway through the first half when Bogdan Stancu blasted his shot from close range over the bar.
But a few minutes later, Stancu was brought down in the penalty area by Estonia defender Mikk Reintam and Marica converted from the spot for his 23rd international goal.
Marica almost doubled Romania's lead after 36 minutes but keeper Sergei Pareiko did well to parry his firm header and Gheorghe Bucur's shot from the edge of the area went narrowly wide five minutes before the break.
Romania's dominance continued in the second half but had to wait until the 81st minute to make the game safe when Marica gave Pareiko no chance with a brilliant header from a precise Alexandru Matel's right-wing cross.