Simon, the top seed and world number 12, was tested more strongly than the score would suggest as he needed almost an hour and a half to finish off the Israeli, who had won his first clay match in over two years to reach the second round.
The 2007 and 2008 champion in Bucharest, Simon kept his nerve on the break points, converting four from six, and now contests his fifth ATP Tour quarter-final of the season.
Seventh-seeded Pole Lukasz Kubot is also through after a 6-3 6-3 win over Romanian wildcard Marius Copil. He faces Simon next.
In other second-round matches there was an upset as Baghdatis crashed out after a tight match with world number 57 Fabio Fognini.
The Italian had been a break down in both sets but triumphed 7-5 7-6(4) over the fifth-seeded Cypriot.
Fognini will face his sixth-seeded compatriot Andreas Seppi, who beat Cedrik-Marcel Stebe 6-2 6-3.
There was another mini-shock as world number 130 Mattias Bachinger beat Troicki 6-3 4-6 7-6(2).
Troicki, the world number 30, was sent packing after a 150-minute epic.
Bachinger plays fellow German Daniel Brands in the quarters, with the final last-eight clash between Attila Balazs of Hungary and Belgium's Xavier Malisse.
They beat Italy's Potito Starace (6-3 6-4) and Germany's Florian Mayer (7-5 4-6 6-4) respectively.
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