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.
In other second-round matches there was an upset as
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
There was another mini-shock as world number 130
Troicki, the world number 30, was sent packing after a 150-minute epic.
Bachinger plays fellow German
They beat Italy's