Grozav's smash-and-grab goal on the break livened up an otherwise dull encounter in Group D, with Liverpool midfielder Nuri Sahin missing the chance to salvage a point at the close.
Romania and Turkey were expected to compete for second place in the pool behind the Netherlands but, with nine points from three games, Victor Piturca's men might just challenge the Oranje for top spot.
Ciprian Tatarusanu was wise to Semih Kaya's bullet header as Turkey tried to seize the initiative in the early exchanges. Emre's free-kick met Umut Bulut, whose effort sailed over the crossbar, and soon Romania came alive.
A smart strike from Ciprian Marica was foiled only by a brave block from Semih Kaya before Grozav made the breakthrough moments before the interval.
Mihai Pintilii launched a perfect through ball beyond the Turkish backline, Volkan Demirel dashing out of his area only to be beaten by Grozav's deft finish from fully 30 yards.
Turkey were stunned into submission but Demirel had to look lively on the hour mark as Gabriel Torje waded into the penalty box.
Mevlut Erdinc was then presented with a gilt-edged chance to level, instead shaving a post, before Arda Turan drew a nervous stop from Tatarusanu.
Six minutes of added time were to be played at the Sukru Saracoglu, but it was not to be Turkey's night as Sahin nodded Turan's pinpoint cross just over the bar.
Romania, yet to concede a goal in the qualifying campaign, go head-to-head with the Dutch on Tuesday.