Anghel Iordanescu’s men, who have conceded only one goal in their eight games, moved up to 16 points, a point behind Group F leaders Northern Ireland and three ahead of third-placed Hungary.
Winless Greece, looking a shadow of the team that won the Euro 2004 title, remained bottom, three points behind fifth-placed Faroe Islands.
A scrappy encounter occasionally burst into life with the Romanians enjoying the better chances but failing to take any of them to the frustration of the National Arena crowd.
Iordanescu made three changes from the starting line-up that managed a goalless draw against Hungary in Budapest on Friday with Constantin Budescu, Alexandru Maxim and Mihai Pintilii replacing Lucian Sanmartean, Adrian Popa and Andrei Prepelita.
Romania dominated possession but lacked the creativity to break down a massed Greek defence.
Budescu, making his first start for Romania after a late appearance on Friday, had a shot blocked by a defender after five minutes and then failed to beat keeper Orestis Karnezis with a low diagonal drive 12 minutes later.
Keseru headed over the bar from close range and then decided to fire a right-footed shot from the edge of the penalty area instead of combining with unmarked Ovidiu Hoban in the closing stages of the first half.
Greece came closest to scoring following a rare attempt on goal from substitute Panagiotis Kone soon after the break while Gabriel Torje forced another excellent save by Karnezis at the other end.
It was the third goalless draw in a row in the qualifying campaign for Romania, who were booed by their fans off the field.
Romania host Finland on Oct. 8 before visiting Faroe Islands in their final qualifier three days later. Greece are away to Northern Ireland and play Hungary at home in their last two games.
(Reporting by Angel Krasimirov, editing by Pritha Sarkar)
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